Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val (n, k) = readLine()!!.split(' ').map { it.toInt() }
    var plusNum = 0
    var minusNum = 0
    var r = LongArray(n+1){ 1 }
    val a = readLine()!!.split(' ').map {
        val num = it.toLong()
        if (num > 0) plusNum++
        else minusNum++
        num
    }


    if (k==n && minusNum%2 == 1 || k%2 == 1 && plusNum == 0) {
        a.sortedBy { Math.abs(it) }
        for (i in 1 .. n) {
            r[i] = modMul(r[i-1], a[i-1])
        }
        println(r[k]+mod)
    } else {
        a.sortedByDescending { Math.abs(it) }
        for (i in 1 .. k) {
            r[i] = modMul(r[i-1], a[i-1])
        }

        var i = k
        if(r[i] < 0) i--
        var j = k
        var ans = r[i]
        while (i < k) {
            if (ans < 0) {
                if (a[j] < 0) {
                    ans = modMul(ans, a[j])
                    i++
                }
            } else {
                if (a[j] > 0) {
                    ans = modMul(ans, a[j])
                    i++
                }
            }
            j++
        }
        println(ans)
    }
}

const val mod = 1000000007L
fun modAdd(a: Long, b:Long):Long = (a + b) % mod
fun modSub(a: Long, b:Long):Long = (a - b) % mod
fun modMul(a: Long, b:Long):Long = (a % mod) * (b % mod) % mod