#include <iostream>
using namespace std;
class z_p {
static int modulus;
int residue; // range from 0 to modulus-1
public:
z_p() {residue = 0;}
z_p(int i) {residue = i % modulus;
            if(residue < 0) residue += modulus;
           }
z_p& operator/(const z_p& b) const
     {return (*this) * b.recip();
     }
z_p& operator*(const z_p& b) const
     {z_p* val_ptr = new z_p;
      val_ptr->residue = residue * b.residue % modulus;
      return(*val_ptr);
     }
z_p& recip(void) const;
friend int main(void);
};// end class z_p

z_p& z_p::recip(void) const
{ // The extended Euclidean algorithm 
  int x, y, q, sx, tx, sy, ty, temp;
  x = modulus; y = residue;
  //*** sx = 1; sy = 0;
  tx = 0; ty = 1;
  while(y != 0)
  // always: gcd(modulus,residue) = gcd(x,y)
  //         sx*modulus + tx*residue = x
  //         sy*modulus + ty*residue = y
       {q = x / y; // integer quotient
        temp = y;  y  = x  - q*y;  x  = temp;
        //*** temp = sy; sy = sx - q*sy; sx = temp;
        temp = ty; ty = tx - q*ty; tx = temp;
       };
  // now x = gcd(modulus,residue)
  z_p* val_prt = new z_p(tx);
  return(*val_prt);
}// end z_p::recip()

/**** test program */
int z_p::modulus = 7;
int main(void)
{cout << (z_p(2)/z_p(4)).residue << endl;
}// end main
/****/