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 PyPy3 (7.3.0) (judge verdict: Accepted)

n = int(input())
a = list(map(int, input().split()))

cum = [0] * n
cum[-1] = a[-1]

mod = 10 ** 9 + 7

for i in range(n - 1, 0, -1):
    cum[i - 1] = cum[i] + a[i - 1]

ans = 0

for i in range(1, n):
    num = a[i - 1] * cum[i]
    num %= mod
    ans += num
    ans %= mod

print(ans)