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 std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let MOD = 100_000_000_0 + 7;
    let n :i64 = read();
    let a :Vec<i64> = (0..n).map(|_| read()).collect();
    let mut ans = 0;
    let mut it = a.iter().rev();
    let la = it.next().unwrap();
    let lb = it.next().unwrap();
    let mut sum = la + lb;
    ans += la * lb;
    loop {
        let next = it.next();
        let mut nextVal = 0;
        match next {
            None => break,
            Some(s) => nextVal = *s,
        };
        ans += nextVal * sum;
        ans %= MOD;
        sum += nextVal;
        sum %= MOD;
    }

    print!("{}", ans);

}