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.

       
#include <iostream>
       
 
       
// return true, if x is a power of two

       
bool isPowerOfTwo(unsigned int x)
       
{
       
  // see http://bits.stephan-brumme.com/isPowerOfTwo.html
       
  return (x & (x - 1)) == 0;
       
}
       
 
       
int main()
       
{
       
  // stop when proportion perfect/total is less than numerator/denominator
       
  unsigned int numerator   = 1;
       
  unsigned int denominator = 12345;
       
  std::cin >> numerator >> denominator;
       
 
       
  if (numerator > denominator || numerator == 0) // check input: for live test only
       
    return 1;
       
 
       
  // count all valid partitions
       
  unsigned long long total   = 1;
       
  // count perfect partitions
       
  unsigned long long perfect = 1;
       
  // x=2^t
       
  unsigned long long x = 3;
       
  // perfect/total > numerator/denominator is the same as
       
  // perfect*denominator > total*numerator
       
  while (perfect * denominator > total * numerator)
       
  {
       
    // found another perfect partition ?
       
    if (isPowerOfTwo(x))
       
      perfect++;
       
 
       
    // keep going ...
       
    total++;
       
    x++;
       
  }
       
 
       
  // find k
       
  unsigned long long k = x * (x - 1);
       
  std::cout << k << std::endl;
       
 
       
  return 0;
       
}

This solution contains 7 empty lines, 11 comments and 1 preprocessor command.