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++ (Clang 10.0.0) (judge verdict: Runtime Error)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <cmath>
using namespace std;
using ll=long long;
#define rep(i,a,b) for(ll i=a;i<ll(b);i++)
#define repr(i,a,b) for(ll i=a;i>=ll(b);i--)
#define endl "\n"
#define ALL(x) x.begin(),x.end()
#define ALLR(x) x.rbegin(),x.rend()
#define INF 1e9
#define DEBUG(x) cout<<"debug: "<<x<<endl

const int MOD = 1000000007;

int n;
int main() {
    cin >> n;
    vector<ll> a(n), b(n+1, 0);
    rep(i, 0, n) cin >> a[i];
    rep(i, 0, n+1) b[i+1] = b[i] + a[i];

    ll ans = 0;
    rep(i, 0, n){
        ll ta = a[i];
        ll tb = b[n] - b[i+1]; tb %= MOD;
        ans += ta*tb;
        ans %= MOD;
    }

    cout << ans << endl;
    return 0;
}