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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program abc50
 implicit none
 integer,allocatable::a(:)
 integer(8),parameter::m=10**9+7
 integer(16)::ia,ans=0,ib,N,ic,id,s
 read(*,*)N
 allocate(a(N))
 read(*,*)(a(ia),ia=1,N)
 s=sum(a)
 do ib=1,N-1
  s=s-a(ib)
  ans=ans+a(ib)*s
 end do
 print'(i0)',mod(ans,m)
end program abc50