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.InputStreamReader
import java.io.PrintWriter
import kotlin.math.abs
import kotlin.math.max

val br = BufferedReader(InputStreamReader(System.`in`))
val out = PrintWriter(System.out)

fun main() {
    br.use { out.use {
        solve()
        out.flush()
    } }
}

val mod = 1000000007

fun Long.mod() = ((this % mod) + mod) % mod

fun solve() {
    val (n, k) = readIntegerList()
    val aList = readLongList().sortedByDescending { abs(it) }

    if (k == n) {
        aList
            .fold(1L) { acc, v -> (acc * v.mod()) % mod }
            .let(out::println)
        return
    }

    val negativeCount = aList.count { it < 0 }
    if (negativeCount == n && k % 2 == 1) {
        aList
            .sortedDescending()
            .take(k)
            .fold(1L) { acc, v -> (acc * v.mod()) % mod }
            .let(out::println)
        return
    }

    val candidateList = aList.take(k)
    val otherList = aList.drop(k)
    val ans = candidateList.fold(1L) { acc, v -> (acc * v.mod()) % mod }
    if (ans >= 0) {
        out.println(ans)
    } else {
        val t1 = candidateList.last { it > 0 }
        val t2 = otherList.last { it < 0 }

        val t3 = candidateList.first { it < 0 }
        val t4 = otherList.first { it > 0 }

        val tmp = candidateList.toLongArray()
        if (t2 * t3 < t4 * t1) {
            tmp[candidateList.indexOf(t1)] = t2
        } else {
            tmp[candidateList.indexOf(t3)] = t4
        }
        tmp
            .fold(1L) { acc, v -> (acc * v.mod()) % mod }
            .let(out::println)
    }
}

fun readInteger() = Integer.parseInt(br.readLine())
fun readLong() = java.lang.Long.parseLong(br.readLine())
fun readStringList() = br.readLine()!!.split(' ')
fun readIntegerList() = readStringList().map(Integer::parseInt)
fun readLongList() = readStringList().map(java.lang.Long::parseLong)
fun readDoubleList() = readStringList().map(java.lang.Double::parseDouble)