<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) {
        priority_queue<long long, vector<long long>, greater<long long>> pq_min;
        priority_queue<long long> pq_max; //max heap, let top() be the n-th ugly number
        unordered_set<long long> st;

        st.insert(1);
        pq_min.push(1);
        pq_max.push(1);

        for (int i = 1; i < n; ++i) {
            long long cur = pq_min.top();
            pq_min.pop();

            for (auto prime: primes) {
                long long next = cur * prime;
                if (st.find(next) != st.end()) {
                    continue;
                }

                if (pq_max.size() >= n) {
                    if (next >= pq_max.top()) {
                        break;
                    } else {
                        pq_max.push(next);
                        pq_max.pop();
                    }
                } else {
                    pq_max.push(next);
                }

                pq_min.push(next);
                st.insert(next);
            }            
        }

        return pq_max.top();
    }
};
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