/*! (c) tom wu | http://www-cs-students.stanford.edu/~tjw/jsbn/
 */
// copyright (c) 2005-2009  tom wu
// all rights reserved.
// see "license" for details.

// extended javascript bn functions, required for rsa private ops.

// version 1.1: new biginteger("0", 10) returns "proper" zero
// version 1.2: square() api, isprobableprime fix

// (public)
function bnclone() { var r = nbi(); this.copyto(r); return r; }

// (public) return value as integer
function bnintvalue() {
  if(this.s < 0) {
    if(this.t == 1) return this[0]-this.dv;
    else if(this.t == 0) return -1;
  }
  else if(this.t == 1) return this[0];
  else if(this.t == 0) return 0;
  // assumes 16 < db < 32
  return ((this[1]&((1<<(32-this.db))-1))<<this.db)|this[0];
}

// (public) return value as byte
function bnbytevalue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }

// (public) return value as short (assumes db>=16)
function bnshortvalue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }

// (protected) return x s.t. r^x < dv
function bnpchunksize(r) { return math.floor(math.ln2*this.db/math.log(r)); }

// (public) 0 if this == 0, 1 if this > 0
function bnsignum() {
  if(this.s < 0) return -1;
  else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
  else return 1;
}

// (protected) convert to radix string
function bnptoradix(b) {
  if(b == null) b = 10;
  if(this.signum() == 0 || b < 2 || b > 36) return "0";
  var cs = this.chunksize(b);
  var a = math.pow(b,cs);
  var d = nbv(a), y = nbi(), z = nbi(), r = "";
  this.divremto(d,y,z);
  while(y.signum() > 0) {
    r = (a+z.intvalue()).tostring(b).substr(1) + r;
    y.divremto(d,y,z);
  }
  return z.intvalue().tostring(b) + r;
}

// (protected) convert from radix string
function bnpfromradix(s,b) {
  this.fromint(0);
  if(b == null) b = 10;
  var cs = this.chunksize(b);
  var d = math.pow(b,cs), mi = false, j = 0, w = 0;
  for(var i = 0; i < s.length; ++i) {
    var x = intat(s,i);
    if(x < 0) {
      if(s.charat(i) == "-" && this.signum() == 0) mi = true;
      continue;
    }
    w = b*w+x;
    if(++j >= cs) {
      this.dmultiply(d);
      this.daddoffset(w,0);
      j = 0;
      w = 0;
    }
  }
  if(j > 0) {
    this.dmultiply(math.pow(b,j));
    this.daddoffset(w,0);
  }
  if(mi) biginteger.zero.subto(this,this);
}

// (protected) alternate constructor
function bnpfromnumber(a,b,c) {
  if("number" == typeof b) {
    // new biginteger(int,int,rng)
    if(a < 2) this.fromint(1);
    else {
      this.fromnumber(a,c);
      if(!this.testbit(a-1))	// force msb set
        this.bitwiseto(biginteger.one.shiftleft(a-1),op_or,this);
      if(this.iseven()) this.daddoffset(1,0); // force odd
      while(!this.isprobableprime(b)) {
        this.daddoffset(2,0);
        if(this.bitlength() > a) this.subto(biginteger.one.shiftleft(a-1),this);
      }
    }
  }
  else {
    // new biginteger(int,rng)
    var x = new array(), t = a&7;
    x.length = (a>>3)+1;
    b.nextbytes(x);
    if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
    this.fromstring(x,256);
  }
}

// (public) convert to bigendian byte array
function bntobytearray() {
  var i = this.t, r = new array();
  r[0] = this.s;
  var p = this.db-(i*this.db)%8, d, k = 0;
  if(i-- > 0) {
    if(p < this.db && (d = this[i]>>p) != (this.s&this.dm)>>p)
      r[k++] = d|(this.s<<(this.db-p));
    while(i >= 0) {
      if(p < 8) {
        d = (this[i]&((1<<p)-1))<<(8-p);
        d |= this[--i]>>(p+=this.db-8);
      }
      else {
        d = (this[i]>>(p-=8))&0xff;
        if(p <= 0) { p += this.db; --i; }
      }
      if((d&0x80) != 0) d |= -256;
      if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
      if(k > 0 || d != this.s) r[k++] = d;
    }
  }
  return r;
}

function bnequals(a) { return(this.compareto(a)==0); }
function bnmin(a) { return(this.compareto(a)<0)?this:a; }
function bnmax(a) { return(this.compareto(a)>0)?this:a; }

// (protected) r = this op a (bitwise)
function bnpbitwiseto(a,op,r) {
  var i, f, m = math.min(a.t,this.t);
  for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
  if(a.t < this.t) {
    f = a.s&this.dm;
    for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
    r.t = this.t;
  }
  else {
    f = this.s&this.dm;
    for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
    r.t = a.t;
  }
  r.s = op(this.s,a.s);
  r.clamp();
}

// (public) this & a
function op_and(x,y) { return x&y; }
function bnand(a) { var r = nbi(); this.bitwiseto(a,op_and,r); return r; }

// (public) this | a
function op_or(x,y) { return x|y; }
function bnor(a) { var r = nbi(); this.bitwiseto(a,op_or,r); return r; }

// (public) this ^ a
function op_xor(x,y) { return x^y; }
function bnxor(a) { var r = nbi(); this.bitwiseto(a,op_xor,r); return r; }

// (public) this & ~a
function op_andnot(x,y) { return x&~y; }
function bnandnot(a) { var r = nbi(); this.bitwiseto(a,op_andnot,r); return r; }

// (public) ~this
function bnnot() {
  var r = nbi();
  for(var i = 0; i < this.t; ++i) r[i] = this.dm&~this[i];
  r.t = this.t;
  r.s = ~this.s;
  return r;
}

// (public) this << n
function bnshiftleft(n) {
  var r = nbi();
  if(n < 0) this.rshiftto(-n,r); else this.lshiftto(n,r);
  return r;
}

// (public) this >> n
function bnshiftright(n) {
  var r = nbi();
  if(n < 0) this.lshiftto(-n,r); else this.rshiftto(n,r);
  return r;
}

// return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
  if(x == 0) return -1;
  var r = 0;
  if((x&0xffff) == 0) { x >>= 16; r += 16; }
  if((x&0xff) == 0) { x >>= 8; r += 8; }
  if((x&0xf) == 0) { x >>= 4; r += 4; }
  if((x&3) == 0) { x >>= 2; r += 2; }
  if((x&1) == 0) ++r;
  return r;
}

// (public) returns index of lowest 1-bit (or -1 if none)
function bngetlowestsetbit() {
  for(var i = 0; i < this.t; ++i)
    if(this[i] != 0) return i*this.db+lbit(this[i]);
  if(this.s < 0) return this.t*this.db;
  return -1;
}

// return number of 1 bits in x
function cbit(x) {
  var r = 0;
  while(x != 0) { x &= x-1; ++r; }
  return r;
}

// (public) return number of set bits
function bnbitcount() {
  var r = 0, x = this.s&this.dm;
  for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
  return r;
}

// (public) true iff nth bit is set
function bntestbit(n) {
  var j = math.floor(n/this.db);
  if(j >= this.t) return(this.s!=0);
  return((this[j]&(1<<(n%this.db)))!=0);
}

// (protected) this op (1<<n)
function bnpchangebit(n,op) {
  var r = biginteger.one.shiftleft(n);
  this.bitwiseto(r,op,r);
  return r;
}

// (public) this | (1<<n)
function bnsetbit(n) { return this.changebit(n,op_or); }

// (public) this & ~(1<<n)
function bnclearbit(n) { return this.changebit(n,op_andnot); }

// (public) this ^ (1<<n)
function bnflipbit(n) { return this.changebit(n,op_xor); }

// (protected) r = this + a
function bnpaddto(a,r) {
  var i = 0, c = 0, m = math.min(a.t,this.t);
  while(i < m) {
    c += this[i]+a[i];
    r[i++] = c&this.dm;
    c >>= this.db;
  }
  if(a.t < this.t) {
    c += a.s;
    while(i < this.t) {
      c += this[i];
      r[i++] = c&this.dm;
      c >>= this.db;
    }
    c += this.s;
  }
  else {
    c += this.s;
    while(i < a.t) {
      c += a[i];
      r[i++] = c&this.dm;
      c >>= this.db;
    }
    c += a.s;
  }
  r.s = (c<0)?-1:0;
  if(c > 0) r[i++] = c;
  else if(c < -1) r[i++] = this.dv+c;
  r.t = i;
  r.clamp();
}

// (public) this + a
function bnadd(a) { var r = nbi(); this.addto(a,r); return r; }

// (public) this - a
function bnsubtract(a) { var r = nbi(); this.subto(a,r); return r; }

// (public) this * a
function bnmultiply(a) { var r = nbi(); this.multiplyto(a,r); return r; }

// (public) this^2
function bnsquare() { var r = nbi(); this.squareto(r); return r; }

// (public) this / a
function bndivide(a) { var r = nbi(); this.divremto(a,r,null); return r; }

// (public) this % a
function bnremainder(a) { var r = nbi(); this.divremto(a,null,r); return r; }

// (public) [this/a,this%a]
function bndivideandremainder(a) {
  var q = nbi(), r = nbi();
  this.divremto(a,q,r);
  return new array(q,r);
}

// (protected) this *= n, this >= 0, 1 < n < dv
function bnpdmultiply(n) {
  this[this.t] = this.am(0,n-1,this,0,0,this.t);
  ++this.t;
  this.clamp();
}

// (protected) this += n << w words, this >= 0
function bnpdaddoffset(n,w) {
  if(n == 0) return;
  while(this.t <= w) this[this.t++] = 0;
  this[w] += n;
  while(this[w] >= this.dv) {
    this[w] -= this.dv;
    if(++w >= this.t) this[this.t++] = 0;
    ++this[w];
  }
}

// a "null" reducer
function nullexp() {}
function nnop(x) { return x; }
function nmulto(x,y,r) { x.multiplyto(y,r); }
function nsqrto(x,r) { x.squareto(r); }

nullexp.prototype.convert = nnop;
nullexp.prototype.revert = nnop;
nullexp.prototype.multo = nmulto;
nullexp.prototype.sqrto = nsqrto;

// (public) this^e
function bnpow(e) { return this.exp(e,new nullexp()); }

// (protected) r = lower n words of "this * a", a.t <= n
// "this" should be the larger one if appropriate.
function bnpmultiplylowerto(a,n,r) {
  var i = math.min(this.t+a.t,n);
  r.s = 0; // assumes a,this >= 0
  r.t = i;
  while(i > 0) r[--i] = 0;
  var j;
  for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
  for(j = math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
  r.clamp();
}

// (protected) r = "this * a" without lower n words, n > 0
// "this" should be the larger one if appropriate.
function bnpmultiplyupperto(a,n,r) {
  --n;
  var i = r.t = this.t+a.t-n;
  r.s = 0; // assumes a,this >= 0
  while(--i >= 0) r[i] = 0;
  for(i = math.max(n-this.t,0); i < a.t; ++i)
    r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
  r.clamp();
  r.drshiftto(1,r);
}

// barrett modular reduction
function barrett(m) {
  // setup barrett
  this.r2 = nbi();
  this.q3 = nbi();
  biginteger.one.dlshiftto(2*m.t,this.r2);
  this.mu = this.r2.divide(m);
  this.m = m;
}

function barrettconvert(x) {
  if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
  else if(x.compareto(this.m) < 0) return x;
  else { var r = nbi(); x.copyto(r); this.reduce(r); return r; }
}

function barrettrevert(x) { return x; }

// x = x mod m (hac 14.42)
function barrettreduce(x) {
  x.drshiftto(this.m.t-1,this.r2);
  if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
  this.mu.multiplyupperto(this.r2,this.m.t+1,this.q3);
  this.m.multiplylowerto(this.q3,this.m.t+1,this.r2);
  while(x.compareto(this.r2) < 0) x.daddoffset(1,this.m.t+1);
  x.subto(this.r2,x);
  while(x.compareto(this.m) >= 0) x.subto(this.m,x);
}

// r = x^2 mod m; x != r
function barrettsqrto(x,r) { x.squareto(r); this.reduce(r); }

// r = x*y mod m; x,y != r
function barrettmulto(x,y,r) { x.multiplyto(y,r); this.reduce(r); }

barrett.prototype.convert = barrettconvert;
barrett.prototype.revert = barrettrevert;
barrett.prototype.reduce = barrettreduce;
barrett.prototype.multo = barrettmulto;
barrett.prototype.sqrto = barrettsqrto;

// (public) this^e % m (hac 14.85)
function bnmodpow(e,m) {
  var i = e.bitlength(), k, r = nbv(1), z;
  if(i <= 0) return r;
  else if(i < 18) k = 1;
  else if(i < 48) k = 3;
  else if(i < 144) k = 4;
  else if(i < 768) k = 5;
  else k = 6;
  if(i < 8)
    z = new classic(m);
  else if(m.iseven())
    z = new barrett(m);
  else
    z = new montgomery(m);

  // precomputation
  var g = new array(), n = 3, k1 = k-1, km = (1<<k)-1;
  g[1] = z.convert(this);
  if(k > 1) {
    var g2 = nbi();
    z.sqrto(g[1],g2);
    while(n <= km) {
      g[n] = nbi();
      z.multo(g2,g[n-2],g[n]);
      n += 2;
    }
  }

  var j = e.t-1, w, is1 = true, r2 = nbi(), t;
  i = nbits(e[j])-1;
  while(j >= 0) {
    if(i >= k1) w = (e[j]>>(i-k1))&km;
    else {
      w = (e[j]&((1<<(i+1))-1))<<(k1-i);
      if(j > 0) w |= e[j-1]>>(this.db+i-k1);
    }

    n = k;
    while((w&1) == 0) { w >>= 1; --n; }
    if((i -= n) < 0) { i += this.db; --j; }
    if(is1) {	// ret == 1, don't bother squaring or multiplying it
      g[w].copyto(r);
      is1 = false;
    }
    else {
      while(n > 1) { z.sqrto(r,r2); z.sqrto(r2,r); n -= 2; }
      if(n > 0) z.sqrto(r,r2); else { t = r; r = r2; r2 = t; }
      z.multo(r2,g[w],r);
    }

    while(j >= 0 && (e[j]&(1<<i)) == 0) {
      z.sqrto(r,r2); t = r; r = r2; r2 = t;
      if(--i < 0) { i = this.db-1; --j; }
    }
  }
  return z.revert(r);
}

// (public) gcd(this,a) (hac 14.54)
function bngcd(a) {
  var x = (this.s<0)?this.negate():this.clone();
  var y = (a.s<0)?a.negate():a.clone();
  if(x.compareto(y) < 0) { var t = x; x = y; y = t; }
  var i = x.getlowestsetbit(), g = y.getlowestsetbit();
  if(g < 0) return x;
  if(i < g) g = i;
  if(g > 0) {
    x.rshiftto(g,x);
    y.rshiftto(g,y);
  }
  while(x.signum() > 0) {
    if((i = x.getlowestsetbit()) > 0) x.rshiftto(i,x);
    if((i = y.getlowestsetbit()) > 0) y.rshiftto(i,y);
    if(x.compareto(y) >= 0) {
      x.subto(y,x);
      x.rshiftto(1,x);
    }
    else {
      y.subto(x,y);
      y.rshiftto(1,y);
    }
  }
  if(g > 0) y.lshiftto(g,y);
  return y;
}

// (protected) this % n, n < 2^26
function bnpmodint(n) {
  if(n <= 0) return 0;
  var d = this.dv%n, r = (this.s<0)?n-1:0;
  if(this.t > 0)
    if(d == 0) r = this[0]%n;
    else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
  return r;
}

// (public) 1/this % m (hac 14.61)
function bnmodinverse(m) {
  var ac = m.iseven();
  if((this.iseven() && ac) || m.signum() == 0) return biginteger.zero;
  var u = m.clone(), v = this.clone();
  var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
  while(u.signum() != 0) {
    while(u.iseven()) {
      u.rshiftto(1,u);
      if(ac) {
        if(!a.iseven() || !b.iseven()) { a.addto(this,a); b.subto(m,b); }
        a.rshiftto(1,a);
      }
      else if(!b.iseven()) b.subto(m,b);
      b.rshiftto(1,b);
    }
    while(v.iseven()) {
      v.rshiftto(1,v);
      if(ac) {
        if(!c.iseven() || !d.iseven()) { c.addto(this,c); d.subto(m,d); }
        c.rshiftto(1,c);
      }
      else if(!d.iseven()) d.subto(m,d);
      d.rshiftto(1,d);
    }
    if(u.compareto(v) >= 0) {
      u.subto(v,u);
      if(ac) a.subto(c,a);
      b.subto(d,b);
    }
    else {
      v.subto(u,v);
      if(ac) c.subto(a,c);
      d.subto(b,d);
    }
  }
  if(v.compareto(biginteger.one) != 0) return biginteger.zero;
  if(d.compareto(m) >= 0) return d.subtract(m);
  if(d.signum() < 0) d.addto(m,d); else return d;
  if(d.signum() < 0) return d.add(m); else return d;
}

var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997];
var lplim = (1<<26)/lowprimes[lowprimes.length-1];

// (public) test primality with certainty >= 1-.5^t
function bnisprobableprime(t) {
  var i, x = this.abs();
  if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
    for(i = 0; i < lowprimes.length; ++i)
      if(x[0] == lowprimes[i]) return true;
    return false;
  }
  if(x.iseven()) return false;
  i = 1;
  while(i < lowprimes.length) {
    var m = lowprimes[i], j = i+1;
    while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
    m = x.modint(m);
    while(i < j) if(m%lowprimes[i++] == 0) return false;
  }
  return x.millerrabin(t);
}

// (protected) true if probably prime (hac 4.24, miller-rabin)
function bnpmillerrabin(t) {
  var n1 = this.subtract(biginteger.one);
  var k = n1.getlowestsetbit();
  if(k <= 0) return false;
  var r = n1.shiftright(k);
  t = (t+1)>>1;
  if(t > lowprimes.length) t = lowprimes.length;
  var a = nbi();
  for(var i = 0; i < t; ++i) {
    //pick bases at random, instead of starting at 2
    a.fromint(lowprimes[math.floor(math.random()*lowprimes.length)]);
    var y = a.modpow(r,this);
    if(y.compareto(biginteger.one) != 0 && y.compareto(n1) != 0) {
      var j = 1;
      while(j++ < k && y.compareto(n1) != 0) {
        y = y.modpowint(2,this);
        if(y.compareto(biginteger.one) == 0) return false;
      }
      if(y.compareto(n1) != 0) return false;
    }
  }
  return true;
}

// protected
biginteger.prototype.chunksize = bnpchunksize;
biginteger.prototype.toradix = bnptoradix;
biginteger.prototype.fromradix = bnpfromradix;
biginteger.prototype.fromnumber = bnpfromnumber;
biginteger.prototype.bitwiseto = bnpbitwiseto;
biginteger.prototype.changebit = bnpchangebit;
biginteger.prototype.addto = bnpaddto;
biginteger.prototype.dmultiply = bnpdmultiply;
biginteger.prototype.daddoffset = bnpdaddoffset;
biginteger.prototype.multiplylowerto = bnpmultiplylowerto;
biginteger.prototype.multiplyupperto = bnpmultiplyupperto;
biginteger.prototype.modint = bnpmodint;
biginteger.prototype.millerrabin = bnpmillerrabin;

// public
biginteger.prototype.clone = bnclone;
biginteger.prototype.intvalue = bnintvalue;
biginteger.prototype.bytevalue = bnbytevalue;
biginteger.prototype.shortvalue = bnshortvalue;
biginteger.prototype.signum = bnsignum;
biginteger.prototype.tobytearray = bntobytearray;
biginteger.prototype.equals = bnequals;
biginteger.prototype.min = bnmin;
biginteger.prototype.max = bnmax;
biginteger.prototype.and = bnand;
biginteger.prototype.or = bnor;
biginteger.prototype.xor = bnxor;
biginteger.prototype.andnot = bnandnot;
biginteger.prototype.not = bnnot;
biginteger.prototype.shiftleft = bnshiftleft;
biginteger.prototype.shiftright = bnshiftright;
biginteger.prototype.getlowestsetbit = bngetlowestsetbit;
biginteger.prototype.bitcount = bnbitcount;
biginteger.prototype.testbit = bntestbit;
biginteger.prototype.setbit = bnsetbit;
biginteger.prototype.clearbit = bnclearbit;
biginteger.prototype.flipbit = bnflipbit;
biginteger.prototype.add = bnadd;
biginteger.prototype.subtract = bnsubtract;
biginteger.prototype.multiply = bnmultiply;
biginteger.prototype.divide = bndivide;
biginteger.prototype.remainder = bnremainder;
biginteger.prototype.divideandremainder = bndivideandremainder;
biginteger.prototype.modpow = bnmodpow;
biginteger.prototype.modinverse = bnmodinverse;
biginteger.prototype.pow = bnpow;
biginteger.prototype.gcd = bngcd;
biginteger.prototype.isprobableprime = bnisprobableprime;

// jsbn-specific extension
biginteger.prototype.square = bnsquare;

// biginteger interfaces not implemented in jsbn:

// biginteger(int signum, byte[] magnitude)
// double doublevalue()
// float floatvalue()
// int hashcode()
// long longvalue()
// static biginteger valueof(long val)