My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#include <iostream>
       
 
       
// limits

       
const unsigned int MaxBlack = 160;
       
const unsigned int MaxWhite = 160;
       
const unsigned int Modulo   = 1000000007; // Hackerrank only
       
 
       
int main()
       
{
       
#define ORIGINAL
       
#ifndef ORIGINAL
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
#endif
       
  {
       
    unsigned int maxBlack = MaxBlack;
       
    unsigned int maxWhite = MaxWhite;
       
    std::cin >> maxBlack >> maxWhite;
       
 
       
    // static array size: actually it would be sufficient to use maxBlack instead of MaxBlack
       
    // (and maxWhite instead of MaxWhite)
       
    unsigned long long previous[MaxBlack + 1][MaxWhite + 1];
       
    unsigned long long current [MaxBlack + 1][MaxWhite + 1];
       
 
       
    // initialize
       
    for (unsigned int i = 0; i <= maxBlack; i++)
       
      for (unsigned int j = 0; j <= maxWhite; j++)
       
        previous[i][j] = 0;
       
    previous[0][0] = 1;
       
 
       
    // all possible subsets
       
    for (unsigned int useBlack = 0; useBlack <= maxBlack; useBlack++)
       
      for (unsigned int useWhite = 0; useWhite <= maxWhite; useWhite++)
       
      {
       
        // skip empty subset
       
        if (useBlack == 0 && useWhite == 0)
       
          continue;
       
 
       
        // put subset at every possible position
       
        for (unsigned int i = 0; i <= maxBlack; i++)
       
          for (unsigned int j = 0; j <= maxWhite; j++)
       
          {
       
            current[i][j] = 0;
       
 
       
            // place it repeatedly
       
            unsigned int k = 0;
       
            while (i >= k * useBlack && j >= k * useWhite)
       
            {
       
              current[i][j] += previous[i - k * useBlack][j - k *  useWhite];
       
              k++;
       
            }
       
#ifndef ORIGINAL
       
            current[i][j] %= Modulo;
       
#endif
       
          }
       
 
       
        // copy for next iteration
       
        for (unsigned int i = 0; i <= maxBlack; i++)
       
          for (unsigned int j = 0; j <= maxWhite; j++)
       
            previous[i][j] = current[i][j];
       
      }
       
 
       
    // print result
       
    std::cout << current[maxBlack][maxWhite] << std::endl;
       
  }
       
 
       
  return 0;
       
}

This solution contains 10 empty lines, 10 comments and 6 preprocessor commands.