# Question

Formatted question description: https://leetcode.ca/all/313.html

```
313 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.
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 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.
@tag-array
```

# Algorithm

Use an idx array to save the current position, and then we take a number from each prime-sub-chain, find the minimum value, and update the corresponding position of the idx array. Note that there may be more than one minimum value. Update the positions of all the minimum values.

# Code

Java