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;

// 
class Main{
    final static int MOD = (int)Math.pow(10, 9) + 7;


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];

        long sum = 0;	// n-1項までの合計
        long ans = 0;
        for(int i = 0; i < N; i++) {
            a[i] = sc.nextInt();
            sum += a[i];
            sum %= MOD;
        }
        
        for(int i = 0; i < N - 1; i++) {
        	sum -= a[i];
        	if(sum < 0) sum += MOD;
            ans += a[i] * sum;
            ans %= MOD;
        }
        
        System.out.println(ans % MOD);
    }

}