<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:
    def countPairs(self, d: List[int]) -> int:
        mod=10**9+7
        def next(n):
            if n <= 0:
                return 1
            
            if (n & (n - 1)) == 0:
                return int(math.log2(n))+1
            
            n -= 1
            n |= n >> 1
            n |= n >> 2
            n |= n >> 4
            n |= n >> 8
            n |= n >> 16
            n += 1
            return int(math.log2(n))
        
        dic={}
        # d.sort()
        lenn=len(d)
        res=0
        summ=0
        
        for i in range(lenn):
            summ+=d[i]
            if i!=0:
                x=next(summ)
                # print(summ,x)
                for j in range(x+1):
                    num=2**j-d[i]
                    if num in dic:
                        # print(num,d[i])
                        res=(res+dic[num])%mod
            
            if d[i] in dic:
                dic[d[i]]+=1
            else:
                dic[d[i]]=1

        return res

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