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: Wrong Answer)

use proconio::{fastout, input};

const MOD_NUM: i64 = 1_000_000_000 + 7;

#[fastout]
fn main() {
    input! {
        n: usize,
        a_vec: [i64; n],
    };
    let mut a_acc = a_vec.iter().fold(0, |acc, a| (acc + a) % MOD_NUM);
    let mut ans = 0;
    for i in 0..a_vec.len() {
        a_acc = (a_acc - a_vec[i]) % MOD_NUM;
        ans = (ans + a_vec[i] * a_acc % MOD_NUM) % MOD_NUM;
    }
    println!("{}", ans);
}