title: Count Possible Paths Top Left Bottom Right Nxm Matrix 2
signature: function count_possible_paths_top_left_bottom_right_nxm_matrix_2(p, q)
test_code: using Printf
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  function validate_solution(actual, expected)
      return actual == expected
  end
  
  function driver(p, q, expected)
      try
  
          if validate_solution(PLACEHOLDER_FN_NAME(p, q), expected)
              return "PASSED";
          end
          return "FAILED";
      catch exception_obj
          return string(Base.typename(typeof(exception_obj)).wrapper);
      end
  end
  
  function main()
      
      result = driver(70, 5, 1088430);
      @printf("TEST-0...%s\n",result);
      
      result = driver(9, 59, 5743572120);
      @printf("TEST-1...%s\n",result);
      
      result = driver(54, 1, 1);
      @printf("TEST-2...%s\n",result);
      
  end
  
  main()
source_py: def count_possible_paths_top_left_bottom_right_nxm_matrix_2(p, q):
      dp = [1 for i in range(q)]
      for i in range((p - 1)):
          for j in range(1, q):
              dp[j] += dp[(j - 1)]
      return dp[(q - 1)]
source_cpp: int count_possible_paths_top_left_bottom_right_nxm_matrix_2(int m, int n) {
    int dp [ n ] = {
      1 };
      dp [ 0 ] = 1;
      for ( int i = 0;
      i < m;
      i ++ ) {
        for ( int j = 1;
        j < n;
        j ++ ) {
          dp [ j ] += dp [ j - 1 ];
        }
      }
      return dp [ n - 1 ];
    }