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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System.Linq;
using static System.Console;

public static class Program
{
    const long mod = 1000000007;
    public static void Main()
    {
        var n = int.Parse(ReadLine());
        var aArray = ReadLine().Split(' ').Select(int.Parse).ToArray();
        long sum = 0;

        long jSum = 0;
        for(int j = 0; j < n; ++j)
        {
            jSum += aArray[j];
            jSum %= mod;
        }
        
        for(int i = 0; i < n - 1; ++i)
        {
            jSum -= aArray[i];
            if (jSum < 0) jSum += mod;
            sum += jSum * aArray[i];
            sum %= mod;
        }
        WriteLine(sum.ToString());
    }
}