// Utils

function assert(val, msg) {
  if (!val)
    throw new Error(msg || 'Assertion failed');
}

function assertEqual(l, r, msg) {
  if (l != r)
    throw new Error(msg || ('Assertion failed: ' + l + ' != ' + r));
}

// Could use `inherits` module, but don't want to move from single file
// architecture yet.
function inherits(ctor, superCtor) {
  ctor.super_ = superCtor
  var TempCtor = function () {}
  TempCtor.prototype = superCtor.prototype
  ctor.prototype = new TempCtor()
  ctor.prototype.constructor = ctor
}

// BN

function BN(number, base) {
  // May be `new BN(bn)` ?
  if (number !== null &&
      typeof number === 'object' &&
      Array.isArray(number.words)) {
    return number;
  }

  this.sign = false;
  this.words = null;
  this.length = 0;

  // Reduction context
  this.red = null;

  if (number !== null)
    this._init(number || 0, base || 10);
}
module.exports = BN;

BN.BN = BN;
BN.wordSize = 26;

BN.prototype._init = function init(number, base) {
  if (typeof number === 'number') {
    if (number < 0) {
      this.sign = true;
      number = -number;
    }
    this.words = [ number & 0x3ffffff ];
    this.length = 1;
    return;
  } else if (typeof number === 'object') {
    // Perhaps a Uint8Array
    assert(typeof number.length === 'number');
    this.length = Math.ceil(number.length / 3);
    this.words = new Array(this.length);
    for (var i = 0; i < this.length; i++)
      this.words[i] = 0;

    // Assume big-endian
    var off = 0;
    for (var i = number.length - 1, j = 0; i >= 0; i -= 3) {
      var w = number[i] | (number[i - 1] << 8) | (number[i - 2] << 16);
      this.words[j] |= (w << off) & 0x3ffffff;
      this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }

    return this.strip();
  }
  if (base === 'hex')
    base = 16;
  assert(base <= 16);

  number = number.toString().replace(/\s+/g, '');
  var start = 0;
  if (number[0] === '-')
    start++;

  if (base === 16)
    this._parseHex(number, start);
  else
    this._parseBase(number, base, start);

  if (number[0] === '-')
    this.sign = true;

  this.strip();
};

BN.prototype._parseHex = function parseHex(number, start) {
  // Create possibly bigger array to ensure that it fits the number
  this.length = Math.ceil((number.length - start) / 6);
  this.words = new Array(this.length);
  for (var i = 0; i < this.length; i++)
    this.words[i] = 0;

  // Scan 24-bit chunks and add them to the number
  var off = 0;
  for (var i = number.length - 6, j = 0; i >= start; i -= 6) {
    var w = parseInt(number.slice(i, i + 6), 16);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
    off += 24;
    if (off >= 26) {
      off -= 26;
      j++;
    }
  }
  if (i + 6 !== start) {
    var w = parseInt(number.slice(start, i + 6), 16);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
  }
  this.strip();
};

BN.prototype._parseBase = function parseBase(number, base, start) {
  // Initialize as zero
  this.words = [ 0 ];
  this.length = 1;

  var word = 0;
  var q = 1;
  var p = 0;
  var bigQ = null;
  for (var i = start; i < number.length; i++) {
    var digit;
    var ch = number[i];
    if (base === 10 || ch <= '9')
      digit = ch | 0;
    else if (ch >= 'a')
      digit = ch.charCodeAt(0) - 97 + 10;
    else
      digit = ch.charCodeAt(0) - 65 + 10;
    word *= base;
    word += digit;
    q *= base;
    p++;

    if (q > 0xfffff) {
      assert(q <= 0x3ffffff);
      if (!bigQ)
        bigQ = new BN(q);
      this.mul(bigQ).copy(this);
      this.iadd(new BN(word));
      word = 0;
      q = 1;
      p = 0;
    }
  }
  if (p !== 0) {
    this.mul(new BN(q)).copy(this);
    this.iadd(new BN(word));
  }
};

BN.prototype.copy = function copy(dest) {
  dest.words = new Array(this.length);
  for (var i = 0; i < this.length; i++)
    dest.words[i] = this.words[i];
  dest.length = this.length;
  dest.sign = this.sign;
  dest.red = this.red;
};

BN.prototype.clone = function clone() {
  var r = new BN(null);
  this.copy(r);
  return r;
};

// Remove leading `0` from `this`
BN.prototype.strip = function strip() {
  while (this.length > 1 && this.words[this.length - 1] === 0)
    this.length--;
  return this._normSign();
};

BN.prototype._normSign = function _normSign() {
  // -0 = 0
  if (this.length === 1 && this.words[0] === 0)
    this.sign = false;
  return this;
};

BN.prototype.inspect = function inspect() {
  return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>';
};

/*
function _zero(n) {
  var code = '';
  for (var i = n - 1; i > 0; i--) {
    var pad = '';
    for (var j = 0; j < n - i; j++)
      pad += '0';
    code += 'if (w.length === ' + i + ') return \'' + pad + '\' + w;\n';
  }
  code += 'return w';

  return new Function('w', code);
}

var zero6 = _zero(6);
var zero14 = _zero(14);
*/

// Sadly chrome apps could not contain `new Function()` calls
function zero6(w) {
  if (w.length === 5) return '0' + w;
  if (w.length === 4) return '00' + w;
  if (w.length === 3) return '000' + w;
  if (w.length === 2) return '0000' + w;
  if (w.length === 1) return '00000' + w;
  return w;
}

function zero14(w) {
  if (w.length === 13) return '0' + w;
  if (w.length === 12) return '00' + w;
  if (w.length === 11) return '000' + w;
  if (w.length === 10) return '0000' + w;
  if (w.length === 9) return '00000' + w;
  if (w.length === 8) return '000000' + w;
  if (w.length === 7) return '0000000' + w;
  if (w.length === 6) return '00000000' + w;
  if (w.length === 5) return '000000000' + w;
  if (w.length === 4) return '0000000000' + w;
  if (w.length === 3) return '00000000000' + w;
  if (w.length === 2) return '000000000000' + w;
  if (w.length === 1) return '0000000000000' + w;
  return w;
}

// Precomputed divisor for `.toString(10)` = 10 ^ 14
var div10 = new BN(null);
div10.words = [ 0x7a4000, 0x16bcc4 ];
div10.length = 2;

BN.prototype.toString = function toString(base) {
  base = base || 10;
  if (base === 16 || base === 'hex') {
    var out = '';
    var off = 0;
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var w = this.words[i];
      var word = (((w << off) | carry) & 0xffffff).toString(16);
      carry = (w >>> (24 - off)) & 0xffffff;
      if (carry !== 0 || i !== this.length - 1)
        out = zero6(word) + out;
      else
        out = word + out;
      off += 2;
      if (off >= 26) {
        off -= 26;
        i--;
      }
    }
    if (carry !== 0)
      out = carry.toString(16) + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else if (base === 10) {
    var out = '';
    var c = this.clone();
    c.sign = false;
    while (c.cmpn(0) !== 0) {
      var r = c.modn(1000000);
      c = c.idivn(1000000);

      if (c.cmpn(0) !== 0)
        out = zero6(r + '') + out;
      else
        out = r + out;
    }
    if (this.cmpn(0) === 0)
      out = '0' + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else {
    assert(false, 'Only 16 and 10 base are supported');
  }
};

BN.prototype.toJSON = function toJSON() {
  return this.toString(16);
};

BN.prototype.toArray = function toArray() {
  this.strip();
  var res = new Array(this.byteLength());
  res[0] = 0;

  var q = this.clone();
  for (var i = 0; q.cmpn(0) !== 0; i++) {
    var b = q.andln(0xff);
    q.ishrn(8);

    // Assume big-endian
    res[res.length - i - 1] = b;
  }

  return res;
};

/*
function genCountBits(bits) {
  var arr = [];

  for (var i = bits - 1; i >= 0; i--) {
    var bit = '0x' + (1 << i).toString(16);
    arr.push('w >= ' + bit + ' ? ' + (i + 1));
  }

  return new Function('w', 'return ' + arr.join(' :\n') + ' :\n0;');
};

BN.prototype._countBits = genCountBits(26);
*/

// Sadly chrome apps could not contain `new Function()` calls
BN.prototype._countBits = function _countBits(w) {
  return w >= 0x2000000 ? 26 :
         w >= 0x1000000 ? 25 :
         w >= 0x800000 ? 24 :
         w >= 0x400000 ? 23 :
         w >= 0x200000 ? 22 :
         w >= 0x100000 ? 21 :
         w >= 0x80000 ? 20 :
         w >= 0x40000 ? 19 :
         w >= 0x20000 ? 18 :
         w >= 0x10000 ? 17 :
         w >= 0x8000 ? 16 :
         w >= 0x4000 ? 15 :
         w >= 0x2000 ? 14 :
         w >= 0x1000 ? 13 :
         w >= 0x800 ? 12 :
         w >= 0x400 ? 11 :
         w >= 0x200 ? 10 :
         w >= 0x100 ? 9 :
         w >= 0x80 ? 8 :
         w >= 0x40 ? 7 :
         w >= 0x20 ? 6 :
         w >= 0x10 ? 5 :
         w >= 0x8 ? 4 :
         w >= 0x4 ? 3 :
         w >= 0x2 ? 2 :
         w >= 0x1 ? 1 :
         0;
};

// Return number of used bits in a BN
BN.prototype.bitLength = function bitLength() {
  var hi = 0;
  var w = this.words[this.length - 1];
  var hi = this._countBits(w);
  return (this.length - 1) * 26 + hi;
};

BN.prototype.byteLength = function byteLength() {
  var hi = 0;
  var w = this.words[this.length - 1];
  return Math.ceil(this.bitLength() / 8);
};

// Return negative clone of `this`
BN.prototype.neg = function neg() {
  if (this.cmpn(0) === 0)
    return this.clone();

  var r = this.clone();
  r.sign = !this.sign;
  return r;
};

// Add `num` to `this` in-place
BN.prototype.iadd = function iadd(num) {
  // negative + positive
  if (this.sign && !num.sign) {
    this.sign = false;
    var r = this.isub(num);
    this.sign = !this.sign;
    return this._normSign();

  // positive + negative
  } else if (!this.sign && num.sign) {
    num.sign = false;
    var r = this.isub(num);
    num.sign = true;
    return r._normSign();
  }

  // a.length > b.length
  var a;
  var b;
  if (this.length > num.length) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    var r = a.words[i] + b.words[i] + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }
  for (; carry !== 0 && i < a.length; i++) {
    var r = a.words[i] + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }

  this.length = a.length;
  if (carry !== 0) {
    this.words[this.length] = carry;
    this.length++;
  // Copy the rest of the words
  } else if (a !== this) {
    for (; i < a.length; i++)
      this.words[i] = a.words[i];
  }

  return this;
};

// Add `num` to `this`
BN.prototype.add = function add(num) {
  if (num.sign && !this.sign) {
    num.sign = false;
    var res = this.sub(num);
    num.sign = true;
    return res;
  } else if (!num.sign && this.sign) {
    this.sign = false;
    var res = num.sub(this);
    this.sign = true;
    return res;
  }

  if (this.length > num.length)
    return this.clone().iadd(num);
  else
    return num.clone().iadd(this);
};

// Subtract `num` from `this` in-place
BN.prototype.isub = function isub(num) {
  // this - (-num) = this + num
  if (num.sign) {
    num.sign = false;
    var r = this.iadd(num);
    num.sign = true;
    return r._normSign();

  // -this - num = -(this + num)
  } else if (this.sign) {
    this.sign = false;
    this.iadd(num);
    this.sign = true;
    return this._normSign();
  }

  // At this point both numbers are positive
  var cmp = this.cmp(num);

  // Optimization - zeroify
  if (cmp === 0) {
    this.sign = false;
    this.length = 1;
    this.words[0] = 0;
    return this;
  }

  // a > b
  if (cmp > 0) {
    var a = this;
    var b = num;
  } else {
    var a = num;
    var b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    var r = a.words[i] - b.words[i] - carry;
    if (r < 0) {
      r += 0x4000000;
      carry = 1;
    } else {
      carry = 0;
    }
    this.words[i] = r;
  }
  for (; carry !== 0 && i < a.length; i++) {
    var r = a.words[i] - carry;
    if (r < 0) {
      r += 0x4000000;
      carry = 1;
    } else {
      carry = 0;
    }
    this.words[i] = r;
  }

  // Copy rest of the words
  if (carry === 0 && i < a.length && a !== this)
    for (; i < a.length; i++)
      this.words[i] = a.words[i];
  this.length = Math.max(this.length, i);

  if (a !== this)
    this.sign = true;

  return this.strip();
};

// Subtract `num` from `this`
BN.prototype.sub = function sub(num) {
  return this.clone().isub(num);
};

/*
// NOTE: This could be potentionally used to generate loop-less multiplications
function _genCombMulTo(alen, blen) {
  var len = alen + blen - 1;
  var src = [
    'var a = this.words, b = num.words, o = out.words, c = 0, w, ' +
        'mask = 0x3ffffff, shift = 0x4000000;',
    'out.length = ' + len + ';'
  ];
  for (var k = 0; k < len; k++) {
    var minJ = Math.max(0, k - alen + 1);
    var maxJ = Math.min(k, blen - 1);

    for (var j = minJ; j <= maxJ; j++) {
      var i = k - j;
      var mul = 'a[' + i + '] * b[' + j + ']';

      if (j === minJ) {
        src.push('w = ' + mul + ' + c;');
        src.push('c = (w / shift) | 0;');
      } else {
        src.push('w += ' + mul + ';');
        src.push('c += (w / shift) | 0;');
      }
      src.push('w &= mask;');
    }
    src.push('o[' + k + '] = w;');
  }
  src.push('if (c !== 0) {',
           '  o[' + k + '] = c;',
           '  out.length++;',
           '}',
           'return out;');

  return src.join('\n');
}
*/

// Multiply `this` by `num` and store data in out
BN.prototype.mulTo = function mulTo(num, out) {
  out.sign = num.sign !== this.sign;
  out.length = this.length + num.length;

  var carry = 0;
  for (var k = 0; k < out.length - 1; k++) {
    // Sum all words with the same `i + j = k` and accumulate `ncarry`,
    // note that ncarry could be >= 0x3ffffff
    var ncarry = carry >>> 26;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - this.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i];
      var b = num.words[j];
      var r = a * b;

      var lo = r & 0x3ffffff;
      ncarry += (r / 0x4000000) | 0;
      lo += rword;
      rword = lo & 0x3ffffff;
      ncarry += lo >>> 26;
    }
    out.words[k] = rword;
    carry = ncarry;
  }
  if (carry !== 0) {
    out.words[k] = carry;
  } else {
    out.length--;
  }

  return out.strip();
};

// Multiply `this` by `num`
BN.prototype.mul = function mul(num) {
  var out = new BN(null);
  out.words = new Array(this.length + num.length);
  return this.mulTo(num, out);
};

// In-place Multiplication
BN.prototype.imul = function imul(num) {
  if (this.cmpn(0) === 0 || num.cmpn(0) === 0) {
    this.words[0] = 0;
    this.length = 1;
    return this;
  }

  var tlen = this.length;
  var nlen = num.length;

  this.sign = num.sign !== this.sign;
  this.length = this.length + num.length;
  this.words[this.length - 1] = 0;

  var lastCarry = 0;
  for (var k = this.length - 2; k >= 0; k--) {
    // Sum all words with the same `i + j = k` and accumulate `carry`,
    // note that carry could be >= 0x3ffffff
    var carry = 0;
    var rword = 0;
    var maxJ = Math.min(k, nlen - 1);
    for (var j = Math.max(0, k - tlen + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i];
      var b = num.words[j];
      var r = a * b;

      var lo = r & 0x3ffffff;
      carry += (r / 0x4000000) | 0;
      lo += rword;
      rword = lo & 0x3ffffff;
      carry += lo >>> 26;
    }
    this.words[k] = rword;
    this.words[k + 1] += carry;
    carry = 0;
  }

  // Propagate overflows
  var carry = 0;
  for (var i = 1; i < this.length; i++) {
    var w = this.words[i] + carry;
    this.words[i] = w & 0x3ffffff;
    carry = w >>> 26;
  }

  return this.strip();
};

// `this` * `this`
BN.prototype.sqr = function sqr() {
  return this.mul(this);
};

// `this` * `this` in-place
BN.prototype.isqr = function isqr() {
  return this.mul(this);
};

// Shift-left in-place
BN.prototype.ishln = function ishln(bits) {
  assert(typeof bits === 'number' && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;
  var carryMask = (0x3ffffff >>> (26 - r)) << (26 - r);

  var o = this.clone();
  if (r !== 0) {
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var newCarry = this.words[i] & carryMask;
      var c = (this.words[i] - newCarry) << r;
      this.words[i] = c | carry;
      carry = newCarry >>> (26 - r);
    }
    if (carry) {
      this.words[i] = carry;
      this.length++;
    }
  }

  if (s !== 0) {
    for (var i = this.length - 1; i >= 0; i--)
      this.words[i + s] = this.words[i];
    for (var i = 0; i < s; i++)
      this.words[i] = 0;
    this.length += s;
  }

  return this.strip();
};

// Shift-right in-place
// NOTE: `hint` is a lowest bit before trailing zeroes
// NOTE: if `extended` is true - { lo: ..., hi: } object will be returned
BN.prototype.ishrn = function ishrn(bits, hint, extended) {
  assert(typeof bits === 'number' && bits >= 0);
  if (hint)
    hint = (hint - (hint % 26)) / 26;
  else
    hint = 0;

  var r = bits % 26;
  var s = Math.min((bits - r) / 26, this.length);
  var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
  var maskedWords = extended;

  hint -= s;
  hint = Math.max(0, hint);

  // Extended mode, copy masked part
  if (maskedWords) {
    for (var i = 0; i < s; i++)
      maskedWords.words[i] = this.words[i];
    maskedWords.length = s;
  }

  if (s === 0) {
    // No-op, we should not move anything at all
  } else if (this.length > s) {
    this.length -= s;
    for (var i = 0; i < this.length; i++)
      this.words[i] = this.words[i + s];
  } else {
    this.words[0] = 0;
    this.length = 1;
  }

  var carry = 0;
  for (var i = this.length - 1; i >= 0 && (carry !== 0 || i >= hint); i--) {
    var word = this.words[i];
    this.words[i] = (carry << (26 - r)) | (word >>> r);
    carry = word & mask;
  }

  // Push carried bits as a mask
  if (maskedWords && carry !== 0)
    maskedWords.words[maskedWords.length++] = carry;

  if (this.length === 0) {
    this.words[0] = 0;
    this.length = 1;
  }

  this.strip();
  if (extended)
    return { hi: this, lo: maskedWords };

  return this;
};

// Shift-left
BN.prototype.shln = function shln(bits) {
  return this.clone().ishln(bits);
};

// Shift-right
BN.prototype.shrn = function shrn(bits) {
  return this.clone().ishrn(bits);
};

// Return only lowers bits of number (in-place)
BN.prototype.imaskn = function imaskn(bits) {
  assert(typeof bits === 'number' && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;

  assert(!this.sign, 'imaskn works only with positive numbers');

  if (r !== 0)
    s++;
  this.length = Math.min(s, this.length);

  if (r !== 0) {
    var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
    this.words[this.length - 1] &= mask;
  }

  return this.strip();
};

// Return only lowers bits of number
BN.prototype.maskn = function maskn(bits) {
  return this.clone().imaskn(bits);
};

// Add plain number `num` to `this`
BN.prototype.iaddn = function iaddn(num) {
  assert(typeof num === 'number');
  if (num < 0)
    return this.isubn(num);
  this.words[0] += num;

  // Carry
  for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) {
    this.words[i] -= 0x4000000;
    if (i === this.length - 1)
      this.words[i + 1] = 1;
    else
      this.words[i + 1]++;
  }
  this.length = Math.max(this.length, i + 1);

  return this;
};

// Subtract plain number `num` from `this`
BN.prototype.isubn = function isubn(num) {
  assert(typeof num === 'number');
  assert(this.cmpn(num) >= 0, 'Sign change is not supported in isubn');
  if (num < 0)
    return this.iaddn(-num);
  this.words[0] -= num;

  // Carry
  for (var i = 0; i < this.length && this.words[i] < 0; i++) {
    this.words[i] += 0x4000000;
    this.words[i + 1] -= 1;
  }

  return this.strip();
};

BN.prototype.addn = function addn(num) {
  return this.clone().iaddn(num);
};

BN.prototype.subn = function subn(num) {
  return this.clone().isubn(num);
};

BN.prototype._wordDiv = function _wordDiv(num, mode) {
  var shift = this.length - num.length;

  var a = this.clone();
  var b = num;

  var q = mode !== 'mod' && new BN(0);
  var sign = false;

  // Approximate quotient at each step
  while (a.length > b.length) {
    // NOTE: a.length is always >= 2, because of the condition .div()
    var hi = a.words[a.length - 1] * 0x4000000 + a.words[a.length - 2];
    var sq = (hi / b.words[b.length - 1]);
    var sqhi = (sq / 0x4000000) | 0;
    var sqlo = sq & 0x3ffffff;
    sq = new BN(null);
    sq.words = [ sqlo, sqhi ];
    sq.length = 2;

    // Collect quotient
    var shift = (a.length - b.length - 1) * 26;
    if (q) {
      var t = sq.shln(shift);
      if (a.sign)
        q.isub(t);
      else
        q.iadd(t);
    }

    sq = sq.mul(b).ishln(shift);
    if (a.sign)
      a.iadd(sq)
    else
      a.isub(sq);
  }
  // At this point a.length <= b.length
  while (a.ucmp(b) >= 0) {
    // NOTE: a.length is always >= 2, because of the condition above
    var hi = a.words[a.length - 1];
    var sq = new BN((hi / b.words[b.length - 1]) | 0);
    var shift = (a.length - b.length) * 26;

    if (q) {
      var t = sq.shln(shift);
      if (a.sign)
        q.isub(t);
      else
        q.iadd(t);
    }

    sq = sq.mul(b).ishln(shift);

    if (a.sign)
      a.iadd(sq);
    else
      a.isub(sq);
  }

  if (a.sign) {
    if (q)
      q.isubn(1);
    a.iadd(b);
  }
  return { div: q ? q : null, mod: a };
};

BN.prototype.divmod = function divmod(num, mode) {
  assert(num.cmpn(0) !== 0);

  if (this.sign && !num.sign) {
    var res = this.neg().divmod(num, mode);
    var div;
    var mod;
    if (mode !== 'mod')
      div = res.div.neg();
    if (mode !== 'div')
      mod = res.mod.cmpn(0) === 0 ? res.mod : num.sub(res.mod);
    return {
      div: div,
      mod: mod
    };
  } else if (!this.sign && num.sign) {
    var res = this.divmod(num.neg(), mode);
    var div;
    if (mode !== 'mod')
      div = res.div.neg();
    return { div: div, mod: res.mod };
  } else if (this.sign && num.sign) {
    return this.neg().divmod(num.neg(), mode);
  }

  // Both numbers are positive at this point

  // Strip both numbers to approximate shift value
  if (num.length > this.length || this.cmp(num) < 0)
    return { div: new BN(0), mod: this };

  // Very short reduction
  if (num.length === 1) {
    if (mode === 'div')
      return { div: this.divn(num.words[0]), mod: null };
    else if (mode === 'mod')
      return { div: null, mod: new BN(this.modn(num.words[0])) };
    return {
      div: this.divn(num.words[0]),
      mod: new BN(this.modn(num.words[0]))
    };
  }

  return this._wordDiv(num, mode);
};

// Find `this` / `num`
BN.prototype.div = function div(num) {
  return this.divmod(num, 'div').div;
};

// Find `this` % `num`
BN.prototype.mod = function mod(num) {
  return this.divmod(num, 'mod').mod;
};

// Find Round(`this` / `num`)
BN.prototype.divRound = function divRound(num) {
  var dm = this.divmod(num);

  // Fast case - exact division
  if (dm.mod.cmpn(0) === 0)
    return dm.div;

  var mod = dm.div.sign ? dm.mod.isub(num) : dm.mod;

  var half = num.shrn(1);
  var r2 = num.andln(1);
  var cmp = mod.cmp(half);

  // Round down
  if (cmp < 0 || r2 === 1 && cmp === 0)
    return dm.div;

  // Round up
  return dm.div.sign ? dm.div.isubn(1) : dm.div.iaddn(1);
};

BN.prototype.modn = function modn(num) {
  assert(num <= 0x3ffffff);
  var p = (1 << 26) % num;

  var acc = 0;
  for (var i = this.length - 1; i >= 0; i--)
    acc = (p * acc + this.words[i]) % num;

  return acc;
};

// In-place division by number
BN.prototype.idivn = function idivn(num) {
  assert(num <= 0x3ffffff);

  var carry = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var w = this.words[i] + carry * 0x4000000;
    this.words[i] = (w / num) | 0;
    carry = w % num;
  }

  return this.strip();
};

BN.prototype.divn = function divn(num) {
  return this.clone().idivn(num);
};

BN.prototype._egcd = function _egcd(x1, p) {
  assert(!p.sign);
  assert(p.cmpn(0) !== 0);

  var a = this;
  var b = p.clone();

  if (a.sign)
    a = a.mod(p);
  else
    a = a.clone();

  var x2 = new BN(0);
  while (a.cmpn(1) > 0 && b.cmpn(1) > 0) {
    while (a.isEven()) {
      a.ishrn(1);
      if (x1.isEven())
        x1.ishrn(1);
      else
        x1.iadd(p).ishrn(1);
    }
    while (b.isEven()) {
      b.ishrn(1);
      if (x2.isEven())
        x2.ishrn(1);
      else
        x2.iadd(p).ishrn(1);
    }
    if (a.cmp(b) >= 0) {
      a.isub(b);
      x1.isub(x2);
    } else {
      b.isub(a);
      x2.isub(x1);
    }
  }
  if (a.cmpn(1) === 0)
    return x1;
  else
    return x2;
};

// Invert number in the field F(num)
BN.prototype.invm = function invm(num) {
  return this._egcd(new BN(1), num).mod(num);
};

BN.prototype.isEven = function isEven(num) {
  return (this.words[0] & 1) === 0;
};

BN.prototype.isOdd = function isOdd(num) {
  return (this.words[0] & 1) === 1;
};

// And first word and num
BN.prototype.andln = function andln(num) {
  return this.words[0] & num;
};

// Increment at the bit position in-line
BN.prototype.bincn = function bincn(bit) {
  assert(typeof bit === 'number');
  var r = bit % 26;
  var s = (bit - r) / 26;
  var q = 1 << r;

  // Fast case: bit is much higher than all existing words
  if (this.length <= s) {
    for (var i = this.length; i < s + 1; i++)
      this.words[i] = 0;
    this.words[s] |= q;
    this.length = s + 1;
    return this;
  }

  // Add bit and propagate, if needed
  var carry = q;
  for (var i = s; carry !== 0 && i < this.length; i++) {
    var w = this.words[i];
    w += carry;
    carry = w >>> 26;
    w &= 0x3ffffff;
    this.words[i] = w;
  }
  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }
  return this;
};

BN.prototype.cmpn = function cmpn(num) {
  var sign = num < 0;
  if (sign)
    num = -num;

  if (this.sign && !sign)
    return -1;
  else if (!this.sign && sign)
    return 1;

  num &= 0x3ffffff;
  this.strip();

  var res;
  if (this.length > 1) {
    res = 1;
  } else {
    var w = this.words[0];
    res = w === num ? 0 : w < num ? -1 : 1;
  }
  if (this.sign)
    res = -res;
  return res;
};

// Compare two numbers and return:
// 1 - if `this` > `num`
// 0 - if `this` == `num`
// -1 - if `this` < `num`
BN.prototype.cmp = function cmp(num) {
  if (this.sign && !num.sign)
    return -1;
  else if (!this.sign && num.sign)
    return 1;

  var res = this.ucmp(num);
  if (this.sign)
    return -res;
  else
    return res;
};

// Unsigned comparison
BN.prototype.ucmp = function ucmp(num) {
  // At this point both numbers have the same sign
  if (this.length > num.length)
    return 1;
  else if (this.length < num.length)
    return -1;

  var res = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var a = this.words[i];
    var b = num.words[i];

    if (a === b)
      continue;
    if (a < b)
      res = -1;
    else if (a > b)
      res = 1;
    break;
  }
  return res;
};

//
// A reduce context, could be using montgomery or something better, depending
// on the `m` itself.
//
BN.red = function red(num) {
  return new Red(num);
};

BN.prototype.toRed = function toRed(ctx) {
  assert(!this.red, 'Already a number in reduction context');
  assert(!this.sign, 'red works only with positives');
  return ctx.convertTo(this)._forceRed(ctx);
};

BN.prototype.fromRed = function fromRed() {
  assert(this.red, 'fromRed works only with numbers in reduction context');
  return this.red.convertFrom(this);
};

BN.prototype._forceRed = function _forceRed(ctx) {
  this.red = ctx;
  return this;
};

BN.prototype.forceRed = function forceRed(ctx) {
  assert(!this.red, 'Already a number in reduction context');
  return this._forceRed(ctx);
};

BN.prototype.redAdd = function redAdd(num) {
  assert(this.red, 'redAdd works only with red numbers');
  return this.red.add(this, num);
};

BN.prototype.redIAdd = function redIAdd(num) {
  assert(this.red, 'redIAdd works only with red numbers');
  return this.red.iadd(this, num);
};

BN.prototype.redSub = function redSub(num) {
  assert(this.red, 'redSub works only with red numbers');
  return this.red.sub(this, num);
};

BN.prototype.redISub = function redISub(num) {
  assert(this.red, 'redISub works only with red numbers');
  return this.red.isub(this, num);
};

BN.prototype.redShl = function redShl(num) {
  assert(this.red, 'redShl works only with red numbers');
  return this.red.shl(this, num);
};

BN.prototype.redMul = function redMul(num) {
  assert(this.red, 'redMul works only with red numbers');
  this.red._verify2(this, num);
  return this.red.mul(this, num);
};

BN.prototype.redIMul = function redIMul(num) {
  assert(this.red, 'redMul works only with red numbers');
  this.red._verify2(this, num);
  return this.red.imul(this, num);
};

BN.prototype.redSqr = function redSqr() {
  assert(this.red, 'redSqr works only with red numbers');
  this.red._verify1(this);
  return this.red.sqr(this);
};

BN.prototype.redISqr = function redISqr() {
  assert(this.red, 'redISqr works only with red numbers');
  this.red._verify1(this);
  return this.red.isqr(this);
};

// Square root over p
BN.prototype.redSqrt = function redSqrt() {
  assert(this.red, 'redSqrt works only with red numbers');
  this.red._verify1(this);
  return this.red.sqrt(this);
};

BN.prototype.redInvm = function redInvm() {
  assert(this.red, 'redInvm works only with red numbers');
  this.red._verify1(this);
  return this.red.invm(this);
};

// Return negative clone of `this` % `red modulo`
BN.prototype.redNeg = function redNeg() {
  assert(this.red, 'redNeg works only with red numbers');
  this.red._verify1(this);
  return this.red.neg(this);
};

BN.prototype.redPow = function redPow(num) {
  assert(this.red && !num.red, 'redPow(normalNum)');
  this.red._verify1(this);
  return this.red.pow(this, num);
};

// Prime numbers with efficient reduction
var primes = {
  k256: null,
  p224: null,
  p192: null,
  p25519: null
};

// Pseudo-Mersenne prime
function MPrime(name, p) {
  // P = 2 ^ N - K
  this.name = name;
  this.p = new BN(p, 16);
  this.n = this.p.bitLength();
  this.k = new BN(1).ishln(this.n).isub(this.p);

  this.tmp = this._tmp();
}

MPrime.prototype._tmp = function _tmp() {
  var tmp = new BN(null);
  tmp.words = new Array(Math.ceil(this.n / 13));
  return tmp;
};

MPrime.prototype.ireduce = function ireduce(num) {
  // Assumes that `num` is less than `P^2`
  // num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P)
  var r = num;
  var rlen;

  do {
    var pair = r.ishrn(this.n, 0, this.tmp);
    r = this.imulK(pair.hi);
    r = r.iadd(pair.lo);
    rlen = r.bitLength();
  } while (rlen > this.n);

  var cmp = rlen < this.n ? -1 : r.cmp(this.p);
  if (cmp === 0) {
    r.words[0] = 0;
    r.length = 1;
  } else if (cmp > 0) {
    r.isub(this.p);
  } else {
    r.strip();
  }

  return r;
};

MPrime.prototype.imulK = function imulK(num) {
  return num.imul(this.k);
};

function K256() {
  MPrime.call(
    this,
    'k256',
    'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f');
}
inherits(K256, MPrime);

K256.prototype.imulK = function imulK(num) {
  // K = 0x1000003d1 = [ 0x40, 0x3d1 ]
  num.words[num.length] = 0;
  num.words[num.length + 1] = 0;
  num.length += 2;
  for (var i = num.length - 3; i >= 0; i--) {
    var w = num.words[i];
    var hi = w * 0x40;
    var lo = w * 0x3d1;
    hi += (lo / 0x4000000) | 0;
    var uhi = (hi / 0x4000000) | 0;
    hi &= 0x3ffffff;
    lo &= 0x3ffffff;

    num.words[i + 2] += uhi;
    num.words[i + 1] += hi;
    num.words[i] = lo;
  }
  var w = num.words[num.length - 2];
  if (w >= 0x4000000) {
    num.words[num.length - 1] += w >>> 26;
    num.words[num.length - 2] = w & 0x3ffffff;
  }
  if (num.words[num.length - 1] === 0)
    num.length--;
  if (num.words[num.length - 1] === 0)
    num.length--;
  return num;
};

function P224() {
  MPrime.call(
    this,
    'p224',
    'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001');
}
inherits(P224, MPrime);

function P192() {
  MPrime.call(
    this,
    'p192',
    'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff');
}
inherits(P192, MPrime);

function P25519() {
  // 2 ^ 255 - 19
  MPrime.call(
    this,
    '25519',
    '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed');
}
inherits(P25519, MPrime);

P25519.prototype.imulK = function imulK(num) {
  // K = 0x13
  var carry = 0;
  for (var i = 0; i < num.length; i++) {
    var hi = num.words[i] * 0x13 + carry;
    var lo = hi & 0x3ffffff;
    hi >>>= 26;

    num.words[i] = lo;
    carry = hi;
  }
  if (carry !== 0)
    num.words[num.length++] = carry;
  return num;
};

// Exported mostly for testing purposes, use plain name instead
BN._prime = function prime(name) {
  // Cached version of prime
  if (primes[name])
    return primes[name];

  var prime;
  if (name === 'k256')
    prime = new K256();
  else if (name === 'p224')
    prime = new P224();
  else if (name === 'p192')
    prime = new P192();
  else if (name === 'p25519')
    prime = new P25519();
  else
    throw new Error('Unknown prime ' + name);
  primes[name] = prime;

  return prime;
}

//
// Base reduction engine
//
function Red(m) {
  if (typeof m === 'string') {
    var prime = BN._prime(m);
    this.m = prime.p;
    this.prime = prime;
  } else {
    this.m = m;
    this.prime = null;
  }
}

Red.prototype._verify1 = function _verify1(a) {
  assert(!a.sign, 'red works only with positives');
  assert(a.red, 'red works only with red numbers');
};

Red.prototype._verify2 = function _verify2(a, b) {
  assert(!a.sign && !b.sign, 'red works only with positives');
  assert(a.red && a.red === b.red,
         'red works only with red numbers');
};

Red.prototype.imod = function imod(a) {
  if (this.prime)
    return this.prime.ireduce(a)._forceRed(this);
  return a.mod(this.m)._forceRed(this);
};

Red.prototype.neg = function neg(a) {
  var r = a.clone();
  r.sign = !r.sign;
  return r.iadd(this.m)._forceRed(this);
};

Red.prototype.add = function add(a, b) {
  this._verify2(a, b);

  var res = a.add(b);
  if (res.cmp(this.m) >= 0)
    res.isub(this.m);
  return res._forceRed(this);
};

Red.prototype.iadd = function iadd(a, b) {
  this._verify2(a, b);

  var res = a.iadd(b);
  if (res.cmp(this.m) >= 0)
    res.isub(this.m);
  return res;
};

Red.prototype.sub = function sub(a, b) {
  this._verify2(a, b);

  var res = a.sub(b);
  if (res.cmpn(0) < 0)
    res.iadd(this.m);
  return res._forceRed(this);
};

Red.prototype.isub = function isub(a, b) {
  this._verify2(a, b);

  var res = a.isub(b);
  if (res.cmpn(0) < 0)
    res.iadd(this.m);
  return res;
};

Red.prototype.shl = function shl(a, num) {
  this._verify1(a);
  return this.imod(a.shln(num));
};

Red.prototype.imul = function imul(a, b) {
  this._verify2(a, b);
  return this.imod(a.imul(b));
};

Red.prototype.mul = function mul(a, b) {
  this._verify2(a, b);
  return this.imod(a.mul(b));
};

Red.prototype.isqr = function isqr(a) {
  return this.imul(a, a);
};

Red.prototype.sqr = function sqr(a) {
  return this.mul(a, a);
};

Red.prototype.sqrt = function sqrt(a) {
  if (a.cmpn(0) === 0)
    return a.clone();

  var mod3 = this.m.andln(3);
  assert(mod3 % 2 === 1);

  // Fast case
  if (mod3 === 3) {
    var pow = this.m.add(new BN(1)).ishrn(2);
    var r = this.pow(a, pow);
    return r;
  }

  // Tonelli-Shanks algorithm (Totally unoptimized and slow)
  //
  // Find Q and S, that Q * 2 ^ S = (P - 1)
  var q = this.m.subn(1);
  var s = 0;
  while (q.cmpn(0) !== 0 && q.andln(1) === 0) {
    s++;
    q.ishrn(1);
  }
  assert(q.cmpn(0) !== 0);

  var one = new BN(1).toRed(this);
  var nOne = one.redNeg();

  // Find quadratic non-residue
  // NOTE: Max is such because of generalized Riemann hypothesis.
  var lpow = this.m.subn(1).ishrn(1);
  var z = this.m.bitLength();
  z = new BN(2 * z * z).toRed(this);
  while (this.pow(z, lpow).cmp(nOne) !== 0)
    z.redIAdd(nOne);

  var c = this.pow(z, q);
  var r = this.pow(a, q.addn(1).ishrn(1));
  var t = this.pow(a, q);
  var m = s;
  while (t.cmp(one) !== 0) {
    var tmp = t;
    for (var i = 0; tmp.cmp(one) !== 0; i++)
      tmp = tmp.redSqr();
    assert(i < m);
    var b = this.pow(c, new BN(1).ishln(m - i - 1));

    r = r.redMul(b);
    c = b.redSqr();
    t = t.redMul(c);
    m = i;
  }

  return r;
};

Red.prototype.invm = function invm(a) {
  var inv = a._egcd(new BN(1), this.m);
  if (inv.sign) {
    inv.sign = false;
    return this.imod(inv).redNeg();
  } else {
    return this.imod(inv);
  }
};

Red.prototype.pow = function pow(a, num) {
  var w = [];
  var q = num.clone();
  while (q.cmpn(0) !== 0) {
    w.push(q.andln(1));
    q.ishrn(1);
  }

  // Skip leading zeroes
  var res = a;
  for (var i = 0; i < w.length; i++, res = this.sqr(res))
    if (w[i] !== 0)
      break;

  if (++i < w.length) {
    for (var q = this.sqr(res); i < w.length; i++, q = this.sqr(q)) {
      if (w[i] === 0)
        continue;
      res = this.mul(res, q);
    }
  }

  return res;
};

Red.prototype.convertTo = function convertTo(num) {
  return num.clone();
};

Red.prototype.convertFrom = function convertFrom(num) {
  var res = num.clone();
  res.red = null;
  return res;
};

//
// Montgomery method engine
//

BN.mont = function mont(num) {
  return new Mont(num);
};

function Mont(m) {
  Red.call(this, m);

  this.shift = this.m.bitLength();
  if (this.shift % 26 !== 0)
    this.shift += 26 - (this.shift % 26);
  this.r = new BN(1).ishln(this.shift);
  this.r2 = this.imod(this.r.sqr());
  this.rinv = this.r.invm(this.m);

  // TODO(indutny): simplify it
  this.minv = this.rinv.mul(this.r)
                       .sub(new BN(1))
                       .div(this.m)
                       .neg()
                       .mod(this.r);
}
inherits(Mont, Red);

Mont.prototype.convertTo = function convertTo(num) {
  return this.imod(num.shln(this.shift));
};

Mont.prototype.convertFrom = function convertFrom(num) {
  var r = this.imod(num.mul(this.rinv));
  r.red = null;
  return r;
};

Mont.prototype.imul = function imul(a, b) {
  if (a.cmpn(0) === 0 || b.cmpn(0) === 0) {
    a.words[0] = 0;
    a.length = 1;
    return a;
  }

  var t = a.imul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).ishrn(this.shift);
  var res = u;
  if (u.cmp(this.m) >= 0)
    res = u.isub(this.m);
  else if (u.cmpn(0) < 0)
    res = u.iadd(this.m);

  return res._forceRed(this);
};

Mont.prototype.mul = function mul(a, b) {
  if (a.cmpn(0) === 0 || b.cmpn(0) === 0)
    return new BN(0)._forceRed(this);

  var t = a.mul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).ishrn(this.shift);
  var res = u;
  if (u.cmp(this.m) >= 0)
    res = u.isub(this.m);
  else if (u.cmpn(0) < 0)
    res = u.iadd(this.m);

  return res._forceRed(this);
};

Mont.prototype.invm = function invm(a) {
  // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
  var res = this.imod(a.invm(this.m).mul(this.r2));
  return res._forceRed(this);
};
