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: Runtime Error)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        new Main();
    }

    public Main() {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] A = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = Integer.parseInt(sc.next());
        }
        long sum = 0;
        long mod = 1000000007;
        long[][] cache = new long[N][N];
        for (int i = 0; i < N; i++) {
            for (int j = i + 1; j < N; j++) {
                if (cache[i][j] == 0) {
                    cache[i][j] = ((A[i] % mod) * (A[j] % mod)) % mod;
                }
                sum = (sum + cache[i][j]) % mod;
            }
        }
        System.out.println(sum);
    }
}