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.io.FileNotFoundException;
import java.math.BigInteger;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {

		//    	File file = new File("src/in.txt");
		//    	Scanner sc = new Scanner(file);

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		BigInteger sum = BigInteger.valueOf(0);
		BigInteger sqsum = BigInteger.valueOf(0);

		for(int i=0;i<N;i++) {
			int A = sc.nextInt();
			BigInteger bigA = BigInteger.valueOf(A);
			sum = sum.add(bigA);
			sqsum = sqsum.add(bigA.pow(2));
		}
		BigInteger sumsq = sum.pow(2);
		BigInteger d = (sumsq.subtract(sqsum)).divide(BigInteger.valueOf(2));

		BigInteger ans = d.mod(BigInteger.valueOf(1000000007));

		System.out.println(ans);
	}
}