github.com/captn3m0/codechef.git

---
category_name: school
problem_code: RGAME
problem_name: 'Rupsa and the Game'
languages_supported:
    - ADA
    - ASM
    - BASH
    - BF
    - C
    - 'C99 strict'
    - CAML
    - CLOJ
    - CLPS
    - 'CPP 4.3.2'
    - 'CPP 4.9.2'
    - CPP14
    - CS2
    - D
    - ERL
    - FORT
    - FS
    - GO
    - HASK
    - ICK
    - ICON
    - JAVA
    - JS
    - 'LISP clisp'
    - 'LISP sbcl'
    - LUA
    - NEM
    - NICE
    - NODEJS
    - 'PAS fpc'
    - 'PAS gpc'
    - PERL
    - PERL6
    - PHP
    - PIKE
    - PRLG
    - PYPY
    - PYTH
    - 'PYTH 3.4'
    - RUBY
    - SCALA
    - 'SCM chicken'
    - 'SCM guile'
    - 'SCM qobi'
    - ST
    - TCL
    - TEXT
    - WSPC
max_timelimit: '1'
source_sizelimit: '50000'
problem_author: abhra73
problem_tester: mgch
date_added: 11-05-2015
tags:
    - abhra73
    - ad
    - easy
    - jan16
editorial_url: 'http://discuss.codechef.com/problems/RGAME'
time:
    view_start_date: 1452504600
    submit_start_date: 1452504600
    visible_start_date: 1452504600
    end_date: 1735669800
    current: 1492507147
layout: problem
---
All submissions for this problem are available.###  Read problems statements in [Mandarin Chinese](http://www.codechef.com/download/translated/JAN16/mandarin/RGAME.pdf), [Russian](http://www.codechef.com/download/translated/JAN16/russian/RGAME.pdf) and [Vietnamese](http://www.codechef.com/download/translated/JAN16/vietnamese/RGAME.pdf) as well.

Princess Rupsa saw one of her friends playing a special game. The game goes as follows:

- **N+1** numbers occur sequentially (one at a time) from **A0** to **AN**.
- You must write the numbers on a sheet of paper, such that **A0** is written first. The other numbers are written according to an inductive rule — after **Ai-1** numbers have been written in a row, then **Ai** can be written at either end of the row. That is, you first write **A0**, and then **A1** can be written on its left or right to make **A0A1** or **A1A0**, and so on.
- **Ai** must be written before writing **Aj**, for every **i < j**.
- For a move in which you write a number **Ai (i>0)**, your points increase by the product of **Ai** and its neighbour. (Note that for any move it will have only one neighbour as you write the number at an end).
- Total score of a game is the score you attain after placing all the **N + 1** numbers.

Princess Rupsa wants to find out the sum of scores obtained by all possible different gameplays. Two gameplays are different, if after writing down all **N + 1** numbers, when we read from left to right, there exists some position **i**, at which the gameplays have **aj** and **ak** written at the **ith** position such that **j ≠ k**. But since she has recently found her true love, a frog Prince, and is in a hurry to meet him, you must help her solve the problem as fast as possible. Since the answer can be very large, print the answer modulo **109 + 7**.

### Input

- The first line of the input contains an integer **T** denoting the number of test cases.
- The first line of each test case contains a single integer **N**.
- The second line contains **N + 1** space-separated integers denoting **A0** to **AN**.

### Output

- For each test case, output a single line containing an integer denoting the answer.

### Constraints

- **1** ≤ **T** ≤ **10**
- **1** ≤ **N** ≤ **105**
- **1** ≤ **Ai** ≤ **109**

### Sub tasks

- Subtask #1: 1 ≤ **N** ≤ 10 (10 points)
- Subtask #2: 1 ≤ **N** ≤ 1000 (20 points)
- Subtask #3: Original Constraints (70 points)

### Example

<pre><b>Input:</b>
2
1
1 2
2
1 2 1

<b>Output:</b>
4
14
</pre>### Explanation

- There are **2** possible gameplays. **A0A1** which gives score of **2** and **A1A0** which also gives score of **2**. So the answer is **2 + 2 = 4**