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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long INF = (long)Math.pow(10, 9) + 7;
        int n = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = sc.nextLong();
        }
        long sum = 0;
        for (int i = 0; i < a.length; i++) {
            sum += a[i];
        }
        long res = 0;
        for (int i = 0; i < a.length - 1; i++) {
            sum -= a[i];
            res += a[i] * (sum % INF);
            res %= INF;
        }
        System.out.println(res);
        sc.close();
    }
}