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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

import scala.io.StdIn._

object Main extends App {

  val n = readInt()
  val A = readLine().split(" ").map(_.toLong)
  def solve() = {
    val mod = (1e9+7).toInt
    (0 until n-1).foldLeft(0L) { (acc, i) =>
      val sum = (i+1 until n).foldLeft(0L) { (accIn, j) =>
        (accIn + A(i) * A(j)) % mod
      }
      (acc + sum) % mod
    } % mod
  }

  println(solve())

}