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>
       
#include <vector>
       
 
       
#define ORIGINAL
       
 
       
// memoized solutions

       
const long long Unknown = -1;
       
std::vector<long long> solutions;
       
 
       
// find result for row with a certain length

       
unsigned long long count(unsigned long long space, unsigned int minBlockLength)
       
{
       
  // finished ?
       
  if (space == 0)
       
    return 1;
       
 
       
  // already know the answer ?
       
  if (solutions[space] != Unknown)
       
    return solutions[space];
       
 
       
  // one option is to leave the next cell black
       
  auto result = count(space - 1, minBlockLength);
       
  // insert red blocks at the current position with all possible spaces
       
  for (auto block = minBlockLength; block <= space; block++)
       
  {
       
    // how much is left after inserting ?
       
    auto next = space - block;
       
    // must be followed by a black cell
       
    if (next > 0)
       
      next--;
       
 
       
    // count all combinations
       
    result += count(next, minBlockLength);
       
  }
       
 
       
  // memoize result
       
  solutions[space] = result;
       
  return result;
       
}
       
 
       
int main()
       
{
       
  unsigned int tests;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    // minimum length of each red block
       
    unsigned int       minBlockLength = 3;
       
    // what number should be exceeded ?
       
    unsigned long long limit          = 1000000;
       
 
       
    std::cin >> minBlockLength >> limit;
       
 
       
    // cached results
       
    solutions.clear();
       
    solutions.resize(limit + 1, Unknown); // not enough for Hackerrank
       
 
       
    for (unsigned int totalLength = 1; ; totalLength++)
       
    {
       
      auto combinations = count(totalLength, minBlockLength);
       
      if (combinations > limit)
       
      {
       
        std::cout << totalLength << std::endl;
       
        break;
       
      }
       
    }
       
  }
       
 
       
  return 0;
       
}

This solution contains 12 empty lines, 13 comments and 3 preprocessor commands.