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: Accepted)

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(n == want) {
			for(int i = 0; i < neg; i++)
				result = (modulo(nega[i], modulo) * result) % modulo;
			for(int i = n - 1; i >= n - pos; i--) {
				result = (posi[i] % modulo * result) % modulo;
			}
		}
		else if(pos != 0) {
			neg = neg / 2 * 2;
			int temp2 = 0;
			int temp = n - 1;
			if(want % 2 == 1) {
				result = result * posi[temp];
				temp--;
				want--;
			}
			while(want > 0 && temp2 < neg && temp > n - pos) {
				if(1l * nega[temp2] * nega[temp2 + 1] >= 1l * posi[temp] * posi[temp - 1]) {
					result *= (1l * nega[temp2] * nega[temp2 + 1]) % modulo; 
					result %= modulo;
					temp2 += 2;
					want -= 2;
				}
				else {
					result *= (1l * posi[temp] * posi[temp - 1]) % modulo; 
					result %= modulo;
					temp -= 2;
					want -= 2;
				}
			}
			
			if(want > 0) {
				while(temp2 < neg && want > 0) {
					result *= (1l * nega[temp2] * nega[temp2 + 1]) % modulo; 
					result %= modulo;
					temp2 += 2;
					want -= 2;
				}
				while(temp > n - pos && want > 0) {
					result *= (1l * posi[temp] * posi[temp - 1]) % modulo; 
					result %= modulo;
					temp -= 2;
					want -= 2;
				}
			}
		}
		else {
			if(want % 2 == 0)
				for(int i = 0; i < want; i++)
					result = (modulo(nega[i], modulo) * result) % modulo;
			else
				for(int i = n - 1; i >= n - want; i--)
					result = (modulo(nega[i], modulo) * result) % modulo;
		}

		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;
	}
}