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: Time Limit Exceeded)


use proconio::{ input, fastout };

#[fastout]
fn main() {
    input! {
        n: i128,
        arr: [i128; n],
    };
    // 0≤i<j≤N-1 を満たす全ての組 (i,j) についての Ai×Aj の和を mod(10^9+7) で求めてください。
    let mut sum: i128 = 0;
    for i in 0..arr.len()-1 {
        for j in i+1..arr.len() {
            sum += arr[i] * arr[j];
        }
    }
    let m: i128 = 10;
    let md = m.pow(9) + 7;
    let ans = sum % md;
    println!("{}", ans);

}