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)

(2) The given numbers in

(3) 0 <

(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.**Understand the problem:**

The idea is very similar to the problem Super ugly number II

Code (Java):

Code (Java):

public class Solution { public int nthSuperUglyNumber(int n, int[] primes) { if (n == 1 || primes == null || primes.length == 0) { return 1; } int k = primes.length; int[] index = new int[k]; List<Integer> result = new ArrayList<>(); result.add(1); for (int i = 1; i < n; i++) { int curr = Integer.MAX_VALUE; for (int j = 0; j < k; j++) { curr = Math.min(curr, primes[j] * result.get(index[j])); } result.add(curr); // update the index for (int j = 0; j < k; j++) { if (primes[j] * result.get(index[j]) == curr) { index[j]++; } } } return result.get(result.size() - 1); } }

**Analysis:**

Time complexity is O(k * n), space complexity is O(n)

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