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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
long long m=1000000007;
int main(){
   int n;
   cin>>n;
   vector<long long> a(n);
   for (int i = 0; i < n; i++)
   {
       cin>>a[i];
   }
   long long sum=0;
   for (int i = 0; i < n; i++)
   {
       for (int j = i+1; j < n; j++)
       {
           sum+=(a[i]*a[j])%m;
       }
       
   }
cout<<sum%m;
   
    return 0;
}