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 Julia (1.4.0) (judge verdict: Runtime Error)

function main()
  n,a=(x->parse.(Int128,split(x))).(readlines())
  s=zeros(Int,n[1])
  for i∈1:n[1]; i>1 && (s[i]=s[i-1]+a[i]); end
  println(sum(INT128[(a[i]*(s[end]-s[i]))%(10^9+7) for i∈1:n[1]-1])%(10^9+7))
end
main()