<p>A <strong>super ugly number</strong> is a positive integer whose prime factors are in the array <code>primes</code>.</p>

<p>Given an integer <code>n</code> and an array of integers <code>primes</code>, return <em>the</em> <code>n<sup>th</sup></code> <em><strong>super ugly number</strong></em>.</p>

<p>The <code>n<sup>th</sup></code> <strong>super ugly number</strong> is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> signed integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 12, primes = [2,7,13,19]
<strong>Output:</strong> 32
<strong>Explanation:</strong> [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].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1, primes = [2,3,5]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= primes.length &lt;= 100</code></li>
	<li><code>2 &lt;= primes[i] &lt;= 1000</code></li>
	<li><code>primes[i]</code> is <strong>guaranteed</strong> to be a prime number.</li>
	<li>All the values of <code>primes</code> are <strong>unique</strong> and sorted in <strong>ascending order</strong>.</li>
</ul>

class Solution {
public:
  int nthSuperUglyNumber(int n, vector<int>& primes) {
    sort(primes.rbegin(),primes.rend());
    priority_queue<long long,vector<long long>,greater<long long>>pq;
    pq.push(1);

    int cnt=n-1;
    while(cnt>0){
      long long temp=pq.top();
      pq.pop();
      cnt--;
      if(temp==1){
        for(int i=0;i<primes.size();i++){
          pq.push(primes[i]*temp);
        }
      }
      else{
        for(int i=0;i<primes.size();i++){
          if(temp%primes[i]==0){
            for(int j=0;j<=i;j++){
              pq.push(primes[j]*temp);
            }
            break;
          }
        }
      }
    }
    return pq.top();
  }
};
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