// CS 1501 Greatest Common Divisor
// Shoup's Iterative code for GCD

long GCD(long a, long b)
{
   long u, v, t, x;

   if (a < 0)
      a = -a;

   if (b < 0)
      b = -b;

   if (a < 0 || b < 0)
      Error("GCD: integer overflow");

   if (b==0)
      x = a;
   else {
      u = a;
      v = b;
      do {
         t = u % v;
         u = v;
         v = t;
      } while (v != 0);

      x = u;
   }

   return x;
}


// Recursive pseudocode for extended GCD

//d = gcd(a, b) = a*s + b*t(d, s, t)
XGCD(long a, long b)
{
   if b==0 return (a, 1, 0)
   else	(d', s', t') = XGCD(b, a mod b)
	(d, s, t) = (d', t', s' - (a/b) *t')
}


// Shoup's iterative code for XGCD
//  d = gcd(a, b) = a*s + b*t;
void XGCD(long& d, long& s, long& t, long a, long b)
{
   long  u, v, u0, v0, u1, v1, u2, v2, q, r;

   long aneg = 0, bneg = 0;
 
   if (a < 0) {
      a = -a;
      aneg = 1;
   }

   if (b < 0) {
      b = -b;
      bneg = 1;
   }

   if (a < 0 || b < 0)
      Error("XGCD: integer overflow");
 
   u1=1; v1=0;
   u2=0; v2=1;
   u = a; v = b;

   while (v != 0) {
      q = u / v;
      r = u % v;
      u = v;
      v = r;
      u0 = u2;
      v0 = v2;
      u2 =  u1 - q*u2;
      v2 = v1- q*v2;
      u1 = u0;
      v1 = v0;
   }

   if (aneg)
      u1 = -u1;

   if (bneg)
      v1 = -v1;

   d = u;
   s = u1;
   t = v1;
}