<p>Given an array of unique integers, <code>arr</code>, where each integer <code>arr[i]</code> is strictly greater than <code>1</code>.</p>

<p>We make a binary tree using these integers, and each number may be used for any number of times. Each non-leaf node&#39;s value should be equal to the product of the values of its children.</p>

<p>Return <em>the number of binary trees we can make</em>. The answer may be too large so return the answer <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [2,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [4, 2, 2]</code></pre>

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

<pre>
<strong>Input:</strong> arr = [2,4,5,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> We can make these trees: <code>[2], [4], [5], [10], [4, 2, 2], [10, 2, 5], [10, 5, 2]</code>.</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>2 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
	<li>All the values of <code>arr</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
 public:
  int numFactoredBinaryTrees(vector<int>& arr) {
    sort(arr.begin(), arr.end());
    int n{static_cast<int>(arr.size())};
    unordered_map<int, int> dp;
    int output{0};

    for (int i = 0; i < n; i++) {
      dp[arr[i]] = 1;

      for (int j = 0; j < i; j++) {
        if (!(arr[i] % arr[j]) && dp.find(arr[i] / arr[j]) != dp.end())
          dp[arr[i]] = (dp[arr[i]] + multiplyWithMod(dp[arr[j]], dp[arr[i] / arr[j]])) % mod;
      }

      output = (output + dp[arr[i]]) % mod;
    }

    return output;
  }

 private:
  static const int mod{1000000007};

  int multiplyWithMod(int a, int b) {
    if (a <= INT_MAX / b)
      return a * b % mod;

    return (multiplyWithMod(a, b / 2) + multiplyWithMod(a, b - b / 2)) % mod;
  }
};
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