Problem Statement  
We define a permutation of an integer N as an integer that has the exact same digits as N, but possibly in a different order. Two permutations of N are considered different if the numbers they represent are not the same. For example, the set of all different permutations of the number N = 313 is {133, 313, 331}. Given a String N and an int M, determine the number of different permutations of N that are divisible by M.  
Definition  
 
Constraints  
  N will contain between 1 and 15 nonzero digits ('1''9'), inclusive.  
  M will be between 1 and 50, inclusive.  
Examples  
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