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# Program to find sum of the 2 power sum of all subarray sums of a given array in Python

Suppose we have a list A. We have taken all non-empty sublists of A as we know a list l with n elements has (2n - 1) non-empty sublist. Now for each sublist, he calculates sublist_sum (the sum of elements and denotes them by S_{1}, S_{2}, S_{3}, ... , S_{(2N-1)}). There is a special sum P such that P = 2^{S1} + 2^{S2} +2^{S3} .... + 2^{S(2N-1)}. We have to find P. If P is too large then return P mod (10^9 + 7).

So, if the input is like A = [2,2,3], then the output will be The subsets are

- {2} so 2^2 = 4
- {2} so 2^2 = 4
- {3} so 2^3 = 8
- {2,2} so 2^4 = 16
- {2,3} so 2^5 = 32
- {2,3} so 2^5 = 32
- {2,2,3} so 2^7 = 128

Sum is 4 + 4 + 8 + 16 + 32 + 32 + 128 = 224

To solve this, we will follow these steps −

- ans:= 1
- m:= 10^9+7
- for each el in A, do
- ans := ans *(1 + (2^el mod m))
- ans := ans mod m

- return (m + ans-1) mod m

## Example

Let us see the following implementation to get better understanding −

def solve(A): ans=1 m=10**9+7 for el in A: ans *= (1+pow(2,el,m)) ans %= m return (m+ans-1) % m A = [2,2,3] print(solve(A))

## Input

[2,2,3]

## Output

224

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