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::input;

const MOD: usize = 1_000_000_007;

fn main() {
  input! {
    n: usize,
    vals: [usize;n]
  }
  
  let mut memo: Vec<usize> = vec![0;n];
  memo[n-1] = vals[n-1] % MOD;
  let mut index = n-2;
  loop {
    memo[index] = memo[index+1] + vals[index] % MOD;
    if index == 0 { break }
    index -= 1;
  }

  let mut result = 0;
  for i in 0..n-1 {
    result = (result + (vals[i] * memo[i+1] % MOD)) % MOD;
  }
  
  println!("{}", result);
}