// Show that the product of two multipliers mod a number is the product of
// each multiplier mod the number.
// Example:  'modulo 4 5 7'
// 4 * 5 mod 7 = 6
// (4 mod 7 * 5 mod 7) mod 7 = 6
#include <iostream>
#include "bigint.h"
using namespace std;

int main (int argc, char **argv) {
   if (argc != 4) {
      cout << "Usage: " << argv[0] << " <num1> <num2> <modulus>\n";
      exit(0);
   }
   
   BigInt num1(atoi(argv[1]));
   BigInt num2(atoi(argv[2]));
   BigInt modulus(atoi(argv[3]));
   cout << num1 << " * " 
	<< num2 << " mod " << modulus << " = " 
	<<  ((num1*num2) % modulus) << "\n";
   cout << "(" << num1 << " mod " << modulus << " * " 
	<< num2 << " mod " << modulus << ") mod " << modulus << " = " 
	<< (((num1 % modulus)*(num2 % modulus)) % modulus) << "\n";
}