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: Accepted)

import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		sc.close();

		int m = 0;
		int z = 0;
		int p = 0;
		for (int i = 0; i < n; i++) {
			if (a[i] == 0) {
				z++;
			} else if (a[i] > 0) {
				p++;
			} else {
				m++;
			}
		}

		boolean bz = false;
		boolean bp = false;
		if (z > 0) {
			bz = true;
		}
		if (p + m == k) {
			if (m % 2 == 0) {
				bp = true;
			}
		} else if (p + m > k) {
			if (p > 0 || k % 2 == 0) {
				bp = true;
			}
		}

		int mod = 1000000007;
		long mod1 = (long) mod * mod;
		if (bp) {
			PriorityQueue<Integer> qp = new PriorityQueue<>((o1, o2) -> o2 - o1);
			PriorityQueue<Integer> qm = new PriorityQueue<>();
			for (int i = 0; i < n; i++) {
				if (a[i] > 0) {
					qp.add(a[i]);
				} else {
					qm.add(a[i]);
				}
			}

			long ans = 1;
			for (int i = 0; i < k; i++) {
				Integer np = qp.poll();
				Integer nm = qm.poll();
				if (np == null) {
					ans *= (long) nm * qm.poll() % mod;
					i++;
				} else if (nm == null) {
					ans *= np;
				} else {
					Integer np2 = qp.poll();
					Integer nm2 = qm.poll();
					if (nm2 == null || i == k - 1) {
						ans *= np;
						if (np2 != null) {
							qp.add(np2);
						}
						qm.add(nm);
					} else if (np2 == null) {
						ans *= (long) nm * nm2 % mod;
						qp.add(np);
						i++;
					} else {
						long vp = (long) np * np2;
						long vm = (long) nm * nm2;
						if (vp > vm) {
							ans *= np;
							qp.add(np2);
							qm.add(nm);
							qm.add(nm2);
						} else {
							ans *= vm % mod;
							qp.add(np);
							qp.add(np2);
							i++;
						}
					}
				}
				if (ans < 0) {
					ans += mod1;
				}
				ans %= mod;
			}
			System.out.println(ans);

		} else if (bz) {
			System.out.println(0);

		} else {
			PriorityQueue<Integer> qp = new PriorityQueue<>();
			PriorityQueue<Integer> qm = new PriorityQueue<>((o1, o2) -> o2 - o1);
			for (int i = 0; i < n; i++) {
				if (a[i] > 0) {
					qp.add(a[i]);
				} else {
					qm.add(a[i]);
				}
			}
			long ans = 1;
			for (int i = 0; i < k; i++) {
				Integer np = qp.peek();
				Integer nm = qm.peek();
				if (nm == null || np != null && np < -nm) {
					ans *= qp.poll();
				} else {
					ans *= qm.poll();
				}
				if (ans < 0) {
					ans += mod1;
				}
				ans %= mod;
			}
			System.out.println(ans);
		}
	}
}