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Super Ugly Number

A super ugly number is a positive integer whose prime factors are in the array primes.

A super ugly number is a positive integer whose prime factors are in the array primes.

Given an integer n and an array of integers primes, return the nth super ugly number.

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

Super Ugly Number diagram

Example 1

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].

Example 2

Input: n = 1, primes = [2,3,5]

Output: 1

Explanation: 1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].

Constraints

  • 1 <= n <= 10^5
  • 1 <= primes.length <= 100
  • 2 <= primes[i] <= 1000
  • primes[i] is guaranteed to be a prime number.
  • All the values of primes are unique and sorted in ascending order.

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