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)

#![allow(unused_imports)]
use proconio::input;
use proconio::marker::*;
const MOD: u64 = 1000000007;
fn main() {
    input!(n: usize, aa: [u64; n]);

    let mut ss = vec![0; n + 1];
    for i in 0..n {
        let idx = n - i;
        ss[idx - 1] = ss[idx] + aa[idx - 1];
        ss[idx - 1] %= MOD;
    }
    let mut sum = 0;
    for i in 0..n {
        let a = aa[i];
        let s = ss[i + 1];
        let tmp = (s * a) % MOD;
        sum += tmp;
        sum %= MOD;
    }
    println!("{}", sum);
}