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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		int p = (int) 1e9 + 7;
		try (Scanner sc = new Scanner(System.in)) {
			int n = Integer.parseInt(sc.next());
			int k = Integer.parseInt(sc.next());
			long[] a = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = Long.parseLong(sc.next());
			}
			Arrays.sort(a);
			int l = 0;
			int r = n - 1;
			long ans = k % 2 == 0 ? 1 : a[r--];
			int b = ans <= 0 ? -1 : 1;

			while (k > 1) {
				long numl = a[l] * a[l + 1] * b;
				long numr = a[r] * a[r - 1] * b;
				if (numl >= numr) {
					ans = ans * (numl % p) % p;
					l = l + 2;
				} else {
					ans = ans * (numr % p) % p;
					r = r - 2;
				}
				k = k - 2;
			}
			System.out.print((ans + p) % p);
		}
	}
}