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 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            final long mod = (long) (1e9 + 7);

            int N = sc.nextInt();
            long[] A = new long[N];
            for (int i = 0; i < N; i++) {
                A[i] = sc.nextInt();
            }

            long[] cumsum = new long[N + 1];
            for (int i = 0; i < N; i++) {
                cumsum[N - 1 - i] += cumsum[N - i] + A[N - 1 - i];
                cumsum[N - 1 - i] %= mod;
            }

            long sum = 0;
            for (int i = 0; i < N; i++) {
                sum += A[i] * cumsum[i + 1];
                sum %= mod;
            }

            System.out.println(sum);
        }
    }
}