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: Time Limit Exceeded)

program C
    implicit none

    integer(4) :: N
    integer(16), allocatable :: A(:) 
    integer(4) :: i, j
    integer(16) :: sum

    read(*, *) N

    allocate(A(1:N))
    read(*, *) A

    sum = 0
    do i = 1, N
        do j = i+1, N
            sum = sum + A(i)*A(j)
            if (sum > 10**9 + 7) then
                sum = mod(sum, 10**9 + 7)
            end if
        end do
    end do

    write(*, *) sum

end program C