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>
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define int long long
#define ld long double
#define vi vector<int>
#define pb push_back
#define ff first
#define ss second
#define all(c) (c).begin(),(c).end()
#define sz(x) (int)(x).size()
#define EPS 0.000000001 //1e-9
#define pii pair<int,int>
using namespace std;
int32_t main()
{
    IOS;
    int n,s=0,p=1000000000+7;
    cin>>n;
    int a[n];
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
    }
    for(int i=0;i<n;i++)
    {
        for(int j=i+1;j<n;j++)
        {
            //int k=((a[i]%p)*(a[j]%p))%p;
            //int k=a[i]*a[j];
            
            s+=(((a[i]%p)*(a[j]%p))%p);
            s=s%p;
        }
    }
    cout << s << endl;
}