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 Ruby (2.7.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>

using namespace std;
using ll = long long int;
using lc = complex<double>;

int main(void) {
    constexpr ll MOD = 1e9 + 7;
    constexpr double PI = acos(-1);
    cout << fixed << setprecision(32);
    cin.tie(0); ios::sync_with_stdio(false);

    ll n;
    cin >> n;
    vector<ll> a(n);
    for(auto &e: a) cin >> e;
    vector<ll> b = a;

    for(ll i=1; i<n; i++)
        b[i] = (b[i-1] + a[i]) % MOD;

    ll res = 0;
    for(ll i=1; i<n; i++)
        (res += (b[i-1] * a[i]) % MOD) %= MOD;
    cout << res << endl;
}