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 OCaml (4.10.0) (judge verdict: Accepted)

let m = 1000000007
let ( +^ ) x y = (x + y) mod m
let ( *^ ) x y = (x * y) mod m

let () = Scanf.scanf "%d\n" @@ fun n ->
  let as_ = Array.init n @@ fun _ -> Scanf.scanf "%d " @@ fun a -> a in
  let acc = Array.make (n + 1) 0 in
  for i = n - 1 downto 0 do
    acc.(i) <- as_.(i) +^ acc.(i + 1)
  done;
  Printf.printf "%d\n" @@
  Array.fold_left ( +^ ) 0 @@
  Array.init (n - 1) @@ fun i -> as_.(i) *^ acc.(i + 1)