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: Accepted)

program main
  implicit none
  integer :: N
  integer(8), allocatable  :: A(:)
  integer :: i,j
  integer(8) :: out, A_sum, idiv
  read(*,*) N
  allocate(A(N))
  read(*,*) A(:)

  out = 0
  !
!!  do i = 1,N-1
!!     do j= i+1,N
!!        out = out + mod(A(i)*A(j),10**9+7)
!!        out = mod(out,10**9+7)
!!     end do
!!  end do
  A_sum = sum(A)
  idiv = int(10**9+7,8)
  do i = 1,N-1
     A_sum = A_sum - A(i)
     out = mod( out + A(i)*mod(A_sum,idiv), idiv ) 
  end do
  write(*,'(i0)') mod(out,idiv)
  deallocate(A)
end program main