<p>A <strong>good meal</strong> is a meal that contains <strong>exactly two different food items</strong> with a sum of deliciousness equal to a power of two.</p>

<p>You can pick <strong>any</strong> two different foods to make a good meal.</p>

<p>Given an array of integers <code>deliciousness</code> where <code>deliciousness[i]</code> is the deliciousness of the <code>i<sup>​​​​​​th</sup>​​​​</code>​​​​ item of food, return <em>the number of different <strong>good meals</strong> you can make from this list modulo</em> <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that items with different indices are considered different even if they have the same deliciousness value.</p>

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

<pre>
<strong>Input:</strong> deliciousness = [1,3,5,7,9]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The good meals are (1,3), (1,7), (3,5) and, (7,9).
Their respective sums are 4, 8, 8, and 16, all of which are powers of 2.
</pre>

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

<pre>
<strong>Input:</strong> deliciousness = [1,1,1,3,3,3,7]
<strong>Output:</strong> 15
<strong>Explanation: </strong>The good meals are (1,1) with 3 ways, (1,3) with 9 ways, and (1,7) with 3 ways.</pre>

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

<ul>
	<li><code>1 &lt;= deliciousness.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= deliciousness[i] &lt;= 2<sup>20</sup></code></li>
</ul>

class Solution {
public:
    int countPairs(vector<int>& deliciousness) {
        set<int> uniques(deliciousness.begin(), deliciousness.end());
        unordered_map<int, int> counts;
        vector<vector<int>> combs;
        long long int tot = 0;
        int max_d = INT_MIN;
        
        for (const auto& d : deliciousness) {
            max_d = max(max_d, d);
            ++counts[d];
        }

        int twos = 1;
        while (true) {
            if (twos - max_d > max_d) break;
            for (const auto& u : uniques) {
                if (twos - u < 0) {
                    break;
                }
                if (uniques.find(twos - u) != uniques.end() && twos - u >= u) {
                    combs.push_back({u, twos - u});
                }
            }
            twos *= 2;
        }

        for (const auto& comb : combs) {
            if (comb[0] == comb[1]) {
                tot = tot + (double) counts[comb[0]] * (counts[comb[0]] - 1) / 2;
            } else {
                tot = tot + (double) counts[comb[0]] * counts[comb[1]];
            }
        }

        int ret = tot % 1000000007;

        return ret;
    }
};
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