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 <stdio.h>
#define MOD 1000000007

int main(void)
{
    int N;
    scanf("%d", &N);

    long A[N];
    long long S[N + 1];
    long long ans = 0;
    for(int i = 0; i < N; i++) { scanf("%ld", &A[i]); }

    S[0] = 0;
    for(int i = 0; i < N; i++) { S[i + 1] = S[i] + A[i]; }

    for(int i = 0; i < N - 1; i++) {
        ans += (A[i] * ((S[N] - S[i + 1]) % MOD));
        ans %= MOD;
    }

    printf("%lld\n", ans);

    return 0;
}