Since the problem set was hard, here is an easy task for you to solve.
You are given an array a consisting of n integers, and your task is to calculate the summation of the multiplication of all subsets of array a. (See the note for more clarifications)
A subset of an array a is defined as a set of elements that can be obtained by deleting zero or more elements from the original array a.
The first line contains an integer T, where T is the number of test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 105), where n is the size of array a.
The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a.
For each test case, print a single line containing the summation of the multiplication of all subsets of array a. Since this number may be too large, print the answer modulo 109 + 7.
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java.
In the first test case, the array a has 6 subsets, and the answer is calculated as follow:
## Input
The first line contains an integer T, where T is the number of test cases.The first line of each test case contains an integer n (1 ≤ n ≤ 105), where n is the size of array a.The second line of each test case contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106), giving the array a.
## Output
For each test case, print a single line containing the summation of the multiplication of all subsets of array a. Since this number may be too large, print the answer modulo 109 + 7.
[samples]
## Note
As input/output can reach huge size it is recommended to use fast input/output methods: for example, prefer to use _scanf/printf_ instead of _cin/cout_ in C++, prefer to use _BufferedReader/PrintWriter_ instead of _Scanner/System.out_ in Java.In the first test case, the array a has 6 subsets, and the answer is calculated as follow: (1) + (2) + (3) + (1 × 2) + (1 × 3) + (2 × 3) + (1 × 2 × 3) = 23.
**Definitions**
Let $ T \in \mathbb{Z} $ be the number of test cases.
For each test case $ k \in \{1, \dots, T\} $:
- Let $ n_k \in \mathbb{Z} $ denote the size of the array.
- Let $ A_k = (a_{k,1}, a_{k,2}, \dots, a_{k,n_k}) $ be a sequence of positive integers.
**Constraints**
1. $ 1 \le T \le 10^5 $
2. For each $ k \in \{1, \dots, T\} $:
- $ 1 \le n_k \le 10^5 $
- $ 1 \le a_{k,i} \le 10^6 $ for all $ i \in \{1, \dots, n_k\} $
**Objective**
For each test case $ k $, compute:
$$
S_k = \sum_{\substack{S \subseteq A_k \\ S \neq \emptyset}} \prod_{x \in S} x \mod (10^9 + 7)
$$
That is, the sum of the products of all non-empty subsets of $ A_k $.