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.

Example:

1 2 3 4

Input: n = 12, primes = [2,7,13,19] Output: 32 Explanation: [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 is a super ugly number for any given primes.

The given numbers in primes are in ascending order.

0 < k ≤ 100, 0 < n ≤ 106, 0 < primes[i] < 1000.

The nth super ugly number is guaranteed to fit in a 32-bit signed integer.

classSolution { public: intnthSuperUglyNumber(int n, std::vector<int>& primes){ auto index = std::vector<int>(primes.size(), 0); auto uglys = std::vector<int>(n, INT_MAX); uglys[0] = 1;

for(auto& ugly : uglys) { for(int i = 0; i < index.size(); i++) { ugly = std::min(ugly, uglys[index[i]] * primes[i]); } for(int i = 0; i < index.size(); i++) { if(ugly == uglys[index[i]] * primes[i]) { index[i]++; } } }