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)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.io.PrintWriter
import java.util.*

// ModInt
// region
class ModInt(x: Long) {

    companion object {
        const val MOD = 1000000007L
        //const val MOD = 998244353L
    }

    val x = (x % MOD + MOD) % MOD

    operator fun plus(other: ModInt): ModInt {
        return ModInt(x + other.x)
    }

    operator fun minus(other: ModInt): ModInt {
        return ModInt(x - other.x)
    }

    operator fun times(other: ModInt): ModInt {
        return ModInt(x * other.x)
    }

    operator fun div(other: ModInt): ModInt {
        return this * other.inv()
    }

    fun pow(exp: Long): ModInt {
        if (exp == 0L) return ModInt(1L)
        var a = pow(exp shr 1)
        a *= a
        if (exp and 1L == 0L) return a
        return this * a
    }

    fun inv(): ModInt {
        return this.pow(MOD - 2)
    }

    override fun equals(other: Any?): Boolean {
        if (this === other) return true
        if (javaClass != other?.javaClass) return false

        other as ModInt

        if (x != other.x) return false

        return true
    }

    override fun hashCode(): Int {
        return x.hashCode()
    }

    override fun toString(): String {
        return "$x"
    }

}

val fac = mutableListOf<ModInt>()
val invfac = mutableListOf<ModInt>()

fun fact(n: Long, b: Boolean): ModInt {
    if (fac.count() == 0) {
        fac.add(ModInt(1))
        invfac.add(ModInt(1))
    }
    while (fac.count() <= n) {
        fac.add(fac.last() * ModInt(fac.count().toLong()))
        invfac.add(fac.last().inv())
    }
    return if (b) {
        fac[n.toInt()]
    } else {
        invfac[n.toInt()]
    }
}

fun comb(n: Long, k: Long): ModInt {
    return fact(n, true) * fact(k, false) * fact(n - k, false)
}

fun comb2(n: Long, k: Long): ModInt {
    var ans = ModInt(1)
    for (i in 0 until k) {
        ans = ans * ModInt(n - i) / ModInt(k - i)
    }
    return ans
}
// endregion

fun PrintWriter.solve(sc: FastScanner) {
    val n = sc.nextInt()
    val k = sc.nextInt()
    val a = Array(n) { sc.nextInt() }
    val lst = mutableListOf<Pair<Long, Boolean>>()
    for (i in 0 until n) {
        lst.add(Math.abs(a[i]).toLong() to (a[i] >= 0))
    }
    lst.sortByDescending { it.first }
    var sign = true
    var v = ModInt(1)
    for (i in 0 until k) {
        v *= ModInt(lst[i].first)
        if (!lst[i].second) {
            sign = !sign
        }
        if (lst[i].first == 0L) sign = true
    }
    if (sign) {
        println(v)
    } else {
        val lst1 = lst.take(k)
        val lst2 = lst.drop(k)
        val pmin = if (lst1.filter { it.second }.count() > 0) { lst1.filter { it.second }.last().first } else -1
        val mmin = if (lst1.filter { !it.second }.count() > 0) { lst1.filter { !it.second }.last().first } else -1
        val pmax = if (lst2.filter { it.second }.count() > 0) { lst2.filter { it.second }.first().first } else -1
        val mmax = if (lst2.filter { !it.second }.count() > 0) { lst2.filter { !it.second }.first().first } else -1
        if (pmin != -1L && mmin != -1L && pmax != -1L && mmax != -1L) {
            if (mmax * mmin >= pmax * pmin) {
                println(v * ModInt(pmax) / ModInt(mmin))
            } else {
                println(v * ModInt(mmax) / ModInt(pmin))
            }
        }
        else if (pmax != -1L && mmin != -1L) {
            println(v * ModInt(pmax) / ModInt(mmin))
        } else if (mmax != -1L && pmin != -1L) {
            println(v * ModInt(mmax) / ModInt(pmin))
        } else {
            v = ModInt(-1)
            lst.sortBy { it.first }
            for (i in 0 until k) {
                v *= ModInt(lst[i].first)
            }
            println(v)
        }
    }
}

fun main() {
    val writer = PrintWriter(System.out, false)
    writer.solve(FastScanner(System.`in`))
    writer.flush()
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}