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Super Ugly Number

Created: September 14, 2019 by [lek-tin]

Last updated: September 14, 2019

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:

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