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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input! {
        n:usize,a: [i64;n]
    }

    let mut ans = 0;
    const MOD: i64 = 1e09 as i64 + 7;
    let mut sum = a.iter().fold(0, |sum, a| sum + a);
    sum %= MOD;

    for i in 0..n {
        sum -= a[i];
        if sum < 0 {
            sum += MOD
        }
        ans += sum * a[i];
        ans %= MOD;
    }
    println!("{}", ans);
}