<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>

#define ll long long
#define MOD 1000000007

class Solution {
public:
    int countPairs(vector<int>& del) {
        int ans = 0;
        vector<ll> goodMeal;
        for(int i = 0; i <= 21; i++) {
            goodMeal.push_back(pow(2, i));
        }

        map<ll, ll> mp;
        for(int i = 0; i < del.size(); i++) {
            mp[del[i]]++;
        }

        for(int i = 0; i < del.size(); i++) {
            ll a = del[i];
            mp[a]--;
            for(int i = 0; i <= 21; i++) {
                ll b = goodMeal[i] - a;
                if(b >= 0) {
                    ans = (ans + mp[b])%MOD;
                }
            }
        }

        return ans;    
    }
};


// goodMeal[] ->  1, 2, 4, 8, 16, 32, 64, 
                                    // del
// a + b = goodMeal
// b = goodMeal - a 

// a/b --> 1, 1, 3, 5, 7, 9, 2^20, 2^20
                    // a
// 1 -> 2
// 3 -> 1
// 5 -> 1
// 7 -> 1
// 9 -> 1
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