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 <math.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define PI acos(-1)
typedef unsigned long long int ull;
typedef long double ld;

int main(void) {
  int   scan;

  ull    answer;
  ull    n;
  ull    *a;
  ull    mod;
  answer = 0;
  mod = 1000000007;
  scan = scanf("%llu", &n);
  a = (ull *)malloc(sizeof(ull) * n);
  for (ull i = 0; i < n; i++) {
    scan = scanf("%llu", &a[i]);
  }

  for (ull i = 0; i < n - 1; i++) {
    for (ull j = i + 1; j < n; j++) {
      answer += (a[i] * a[j]) % mod;
    }
  }

  answer = answer % mod;

  printf("%llu", answer);

  return (0);
}