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, fastout};
use proconio::marker::{Chars};
use proconio::marker::Usize1;
use std::cmp::*;

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
  }

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

    let mut sum = 0;
    for i in 1..n {
        sum += a[i];
    }
    debug!(sum);
    let inf = 10_0000_0000 + 7;
    sum %= inf;

    let mut ans = 0;
    for i in 0..n-1 {
        ans += a[i]*sum;
        ans %= inf;
        sum = sum + inf - a[i+1];
        sum %= inf;
        debug!(sum);
        debug!(ans);
    }

    println!("{}", ans);

}