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: Accepted)

#include<bits/stdc++.h>

using namespace std;
const int mod = 1e9 + 7;

int main() {
    int n; cin >> n; int arr[n];
    for (int i = 0; i < n; i++) cin >> arr[i];
    long long int suffix[n]; suffix[n - 1] = arr[n - 1];
    for (int i = n - 2; i >= 0; i--) {
        suffix[i] = (suffix[i + 1] + arr[i]) % mod;
    }
    long long int ans = 0;
    for (int i = 0; i < n - 1; i++) {
        ans += (1LL * arr[i] * suffix[i + 1]) % mod;
    }
    cout << ans % mod;
    return 0;
}