Super ugly number

Write a program to find the nth super ugly number.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k. For example, [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32] is the sequence of the first 12 super ugly numbers given primes = [2, 7, 13, 19] of size 4.

Note:
(1) 1 is a super ugly number for any given primes.
(2) The given numbers in primes are in ascending order.
(3) 0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.

class Solution {
public:   int nthSuperUglyNumber(int n, vector<int>& primes) { 
      int len = primes.size();       
      vector<int> mult(len,0);       
      vector<int> super_ugly(n,INT_MAX);       
      super_ugly[0] = 1;       
      for (int i = 1; i < n; ++i) {         
         for (int j = 0; j < len; ++j)                
            super_ugly[i] = min(super_ugly[i],super_ugly[mult[j]] * primes[j]);              for(int j = 0; j < len; ++j)                 
             if (super_ugly[i] == super_ugly[mult[j]] * primes[j]) {                                 ++mult[j];                 
             }       
         }       
      return super_ugly[n-1];          
      }
};