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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.math.BigInteger;
import java.util.*;

public class Main {

  private static final BigInteger MOD = BigInteger.valueOf(1000000007);

  public static void main(String[] args) {
    int n = scanner.nextInt();
    int k = scanner.nextInt();
    int[] A = new int[n];
    for (int i = 0; i < n; i++) {
      A[i] = scanner.nextInt();
    }
    List<Integer> pos = new ArrayList<>();
    List<Integer> neg = new ArrayList<>();
    int zero = 0;
    long all = 1;
    for (int i : A) {
      if (i > 0) {
        pos.add(i);
      } else if (i < 0) {
        neg.add(i);
      } else {
        zero++;
      }
      all = (all * i) % MOD.intValue();
    }
    if (pos.size() + neg.size() < k || (n == k && zero > 0)) {
      System.out.println(0);
      return;
    }
    if (n == k) {
      System.out.println(Math.floorMod(all, MOD.intValue()));
      return;
    }
    pos.sort(Comparator.reverseOrder());
    neg.sort(Comparator.reverseOrder());
    BigInteger[] posMulLft = new BigInteger[pos.size() + 1];
    BigInteger[] negMulLft = new BigInteger[neg.size() + 1];
    BigInteger[] negMulRgt = new BigInteger[neg.size() + 1];
    posMulLft[0] = BigInteger.ONE;
    negMulLft[0] = BigInteger.ONE;
    negMulRgt[negMulRgt.length - 1] = BigInteger.ONE;
    for (int i = 1; i < Math.min(k + 1, posMulLft.length); i++) {
      posMulLft[i] = posMulLft[i - 1].multiply(BigInteger.valueOf(pos.get(i - 1)));
    }
    for (int i = 1; i < Math.min(k + 1, negMulLft.length); i++) {
      negMulLft[i] = negMulLft[i - 1].multiply(BigInteger.valueOf(neg.get(i - 1)));
    }
    for (int i = negMulRgt.length - 2, j = k; i >= 0 && j >= 0; i--, j--) {
      negMulRgt[i] = negMulRgt[i + 1].multiply(BigInteger.valueOf(neg.get(i)));
    }
    BigInteger res = BigInteger.valueOf(Long.MIN_VALUE);
    for (int i = 0; i < Math.min(k + 1, posMulLft.length); i++) {
      if (k - i < negMulLft.length) {
        res = posMulLft[i].multiply(negMulLft[k - i]).max(res);
      }
    }
    for (int i = 0; i < Math.min(k + 1, negMulRgt.length); i++) {
      if (k - i < posMulLft.length) {
        res = negMulRgt[negMulRgt.length - 1 - i].multiply(posMulLft[k - i]).max(res);
      }
    }
    System.out.println(res.mod(MOD));
  }

  private static final Scanner scanner = new Scanner(System.in);
}