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.util.*;
import java.io.*;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		ArrayList<Integer> arr = new ArrayList<Integer>();
		boolean allneg = true;
		int mod=(int) (1e9+7);
		int numneg = 0;
		int numpos = 0;
		for(int i = 0; i < n; i++)
		{
			int x = in.nextInt();
			arr.add(x);
			if(x > 0) 
			{
				allneg = false;
				numpos++;
			}
			else numneg++;
		}
		Collections.sort(arr, (a, b) -> Math.abs(b) - Math.abs(a));
		
		long sum = 1;
		if(n == k)
			for(int i = 0; i < n; i++)
			{
				sum *= arr.get(i);
				sum %= mod;
			}
		else if(allneg)
		{
			if(k % 2 == 1)
				for(int i = n - 1; i >= n - k; i--)
				{
					sum *= arr.get(i);
					sum %= mod;
				}
			else
				for(int i = 0; i < k; i++)
				{
					sum *= arr.get(i);
					sum %= mod;
				}
		}
		else
		{
			Queue<Integer> q = new LinkedList<Integer>();
			boolean[] vis = new boolean[n];
			for(int i = 0; i < n; i++)
			{
				if(q.size() > k) break;
				if(vis[i]) continue;
				
				if(numpos == 1)
				{
					for(int j = i + 1; j < n; j++)
						if(arr.get(j) > 0) 
						{
							vis[j] = true;
							q.add(arr.get(j));
							numpos --;
							break;
						}
				}
				if(arr.get(i) < 0)
				{
					if(numneg == 1) 
						continue;
					q.add(arr.get(i));
					vis[i] = true;
					for(int j = i + 1; j < n; j++)
						if(arr.get(j) < 0) 
						{
							vis[j] = true;
							q.add(arr.get(j));
							numneg -= 2;
							break;
						}
				}
				else
				{
					if(!(numpos == 0))
					{
						q.add(arr.get(i));
						vis[i] = true;
						numpos--;
					}
				}
			}
			
			for(int i = 0; i < k; i++)
			{
				sum *= q.poll();
				sum %= mod;
			}
			
		}
		if(sum < 0) sum += mod;
		System.out.println(sum);
		
		
		
		
		
		

	}
}