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)

Scanf.scanf "%d" (fun n ->
    let z = 1000000007 in
    let extgcd x y =
        let rec eg r0 r1 a0 a1 b0 b1 =
            if r1 = 0 then a0 else
                let q1 = r0 / r1 in
                eg r1 (r0 mod r1) a1 (a0 - q1 * a1) b1 (b0 - q1 * b1)
        in
        eg x y 1 0 0 1
    in
    let inv x y = (* 1/x in mod y *)
        let c = extgcd x y in
        if c < 0 then c + y else c
    in

    let ( +@) a b = (a + b) mod z in
    let ( -@) a b = (((a - b) mod z) + z) mod z in
    let ( *@) a b = (a * b) mod z in
    let ( /@) a b = a *@ inv b z in
    let a = Array.init n (fun _ -> Scanf.scanf " %d" (fun a -> a)) in
    let k = Array.fold_left (fun acc a -> acc +@ a * a) 0 a in
    let s = Array.fold_left (+@) 0 a in
    Printf.printf "%d\n" @@ (s *@ s -@ k) /@ 2
)