Problem:
Score : 300 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

Find the sum of A_i \times A_j over all pairs (i,j) such that 1\leq i < j \leq N, modulo (10^9+7).

Constraints

2 \leq N \leq 2\times 10^5

0 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

Print \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

11

We have 1 \times 2 + 1 \times 3 + 2 \times 3 = 11.

Sample Input 2

4
141421356 17320508 22360679 244949

Sample Output 2

437235829

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

const main = (input) => {
  input = input.trim().split('\n')
  const mod = 10n**9n + 7n
  const arr = input[1].split(' ').map(BigInt).sort((a, b) => b - a)

  let sum = arr[0] + arr[1]
  let ans = arr[0] * arr[1] % mod

  for (let i=2; i<arr.length; i++) {
    ans += sum * arr[i] % mod
    sum += arr[i]
  }

  return console.log(`${ans % mod}`)
}

process.env.MYTEST ? test() : main(require('fs').readFileSync('/dev/stdin', 'utf8'))