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.*;
public class Main{
  public static void main(String[] args){
    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(); 
    }
    System.out.println(maxProduct(a, n, k));
  }
  
  public static int maxProduct(int[] a, int n, int k){
   	Arrays.sort(a);
    int product = 1;
    if(a[n-1] == 0 && k%2 != 0){
      return 0; 
    }
    if(a[n-1] <= 0 && k%2 != 0){
      for(int i=n-1;i>=n;i--){
        product *= a[i]%1000000007; 
      }
      return product;
    }
    int i = 0;
    int j = n-1;
    if(k%2 != 0){
      product *= a[j]%1000000007;
      j--;
      k--;
    }
    k >>= 1;
    for(int t=0;t<k;t++){
      int left = a[i]*a[i+1];
      int right = a[j]*a[j-1];
      if(left > right){
       	product *= left%1000000007;
        i += 2;
      }else{
        product *= right%1000000007;
        j -= 2;
      }
    }
    return product;
  }
}