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 x=0;
    int y=0;
    int z =0;
    int w=N-1;
    long ans =1;
    int q=K%2;
    int Q =K/2;
    long R;long S;
    long A[] =new long[N];
    for(int i=0;i<N;i++){
      A[i]=sc.nextLong();
      if(A[i]<=0){x=x+1;}
      if(A[i]==0){y=y+1;}}
    Arrays.sort(A);
    if((q==1)&&(x==N)){
      if(y!=0){System.out.println(0);}
      else{
        for(int j=N-1;j>=N-K;j--){
          ans =ans*A[j];
          ans =ans%1000000007;}
        ans =ans+1000000007;
        System.out.println(ans);}
    }
    else if(x!=0){{
      for(int k=0;k<K;k++){
          R =A[z]*A[z+1];
          S =A[w]*A[w-1];
          if(R>=S){K=K-2;
            ans =ans*R;
            if(ans<0){
              ans =ans%1000000007;
              ans =ans*(-1)+291172353;}
            else{ans =ans%1000000007;}
            z=z+2;}
          else{K=K-1;
            ans =ans*A[w];
            if(ans<0){ans =ans%1000000007;ans =ans*(-1)+291172353;}
            else{ans =ans%1000000007;}
            w=w-1;}
        }
      if(q==0){System.out.println(ans);}
      else{
        ans =ans*A[w];
        ans =ans%1000000007;
        System.out.println(ans);}
    }}
    else{
      for(int m=N-1;m>N-K;m--){
      ans =ans*A[m];
        if(ans<0){
              ans =ans%1000000007;
              ans =ans*(-1)+291172353;}
        else{ans =ans%1000000007;}
      }
      System.out.println(ans);
    }
  }
}