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 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedWriter;
import java.io.File;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws IOException{
		Scanner scanner = new Scanner(System.in);
		int modulo = (int) 1e9 + 7;
		int n = scanner.nextInt();
		int want = scanner.nextInt();
		int pos = 0;
		int neg = 0;
		int[] nega = new int[n];
		int[] posi = new int[n];
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		for(int i = 0; i < n; i++) {
			int temp = scanner.nextInt();
			if(temp < 0) {
				nega[neg] = temp;
				neg++;
			}
			else {
				posi[pos] = temp;
				pos++;
			}
		}
		Arrays.sort(nega);
		Arrays.sort(posi);
		long result = 1l;
		if(want % 2 == 1 && pos > 0) {
			result *= 1l * posi[n - 1];
			pos--;
			want--;
		}
		while(want > 0 && neg > 1 && pos > 1) {
			long temp1 = posi[n - 1] * posi[n - 2];
			long temp2 = nega[neg - 1] * nega[neg - 2];
			if(temp1 > temp2) {
				result *= 1l * (temp1 % modulo);
				pos -= 2;
				n -= 2;
			}
			else {
				result *= 1l * (temp2 % modulo);
				neg -= 2;
				result %= modulo;
			}
			want -= 2;
		}
		if(want != 0) {
			while(want > 0 && pos > 0) {
				result = 1l * (result * (posi[n - 1] % modulo)) % modulo;
				pos--;
				want--;
				n--;
			}
			
			while(want > 0 && neg > 0) {
				int temp = modulo(nega[neg - 1], modulo);
				result = 1l * (result * temp) % modulo;
				neg--;
				want--;
			}
		}
		log.write("" + result);
		log.flush();
	}

	private static int modulo(int i, int modulo) {
		if(i < 0)
			i *= -1;
		i %= modulo;
		if(i == 0)
			return 0;
		return modulo - i;
	}
}