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;
using System.Collections.Generic;
using System.Linq;

class Program
{
  static void Main(string[] args)
  {
    const UInt64 modNum = 1000000007;

    uint N = uint.Parse(Console.ReadLine());
    string[] items = Console.ReadLine().Split(' ');

    UInt64[] A = Array.ConvertAll(items, UInt64.Parse);

    UInt64 sum = 0;
    UInt64 sumPartOfA = 0;

    //From back.
    for (int i = (int)N - 1; i > 0; --i)
    {
      sumPartOfA += A[i];
      sumPartOfA %= modNum;
      sum += (A[i - 1] * sumPartOfA) % modNum;
    }

    sum %= modNum;

    Console.WriteLine(sum);

    return;
  }
}