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: Wrong Answer)

fun main() {
    readLine()
    val x = readLine()!!.split(" ").map(String::toLong)
    val s = x.toMutableList()

    (1 until x.size).forEach { i -> s[i] = (s[i] + s[i - 1]).rem(1000000007) }

    x.indices.map { i -> (x[i] * (s.last() - s[i])).rem(1000000007) }
            .reduce { acc, i ->  (acc + i).rem(1000000007) }
            .let { println(it) }
}