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)



const val m = 1000000007L
fun main(args: Array<String>) {
    val n = getInt()
    val a = getLongs()
    var sum = 0L
    a.forEach {
        sum = (sum + it) % m
    }

    var out = 0L
    a.forEach {
        out = (out + (sum - it) * it) % m
    }
    println(out * inv(2) % m)
}

fun inv(k: Long): Long {
    return pow(k, m - 2)
}

fun pow(k: Long, p: Long): Long {
    return when {
        p == 0L -> 1
        p == 1L -> k
        p % 2L == 0L -> pow(k, p / 2L).let { it * it % m }
        else -> pow(k, p / 2L).let { (it * it % m) * k % m }
    }
}

fun getInt() = readLine()!!.toInt()
fun getInts() = readLine()!!.split(" ").map { it.toInt() }
fun getLong() = readLine()!!.toLong()
fun getLongs() = readLine()!!.split(" ").map { it.toLong() }