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 Kotlin (1.3.71) (judge verdict: Accepted)

const val MOD = 1000000007L

fun main() {
  val N = readInt()
  val AN = readLongs()

  val SN = Array(N) { 0L }
  SN[0] = AN[0]
  for (i in 1 until N) {
    SN[i] = SN[i - 1] + AN[i]
  }

  var result = 0L
  for (i in 0 until N - 1) {
    result = (result + (AN[i] * ((SN.last() - SN[i]) % MOD)) % MOD) % MOD
  }
  println(result)
}

fun readString() = readLine()!!
fun readStrings() = readString().split(" ")
fun readInt() = readString().toInt()
fun readLong() = readString().toLong()
fun readInts() = readStrings().map { it.toInt() }
fun readLongs() = readStrings().map { it.toLong() }