Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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

public class Main{
	public static void main(String[] args)  throws IOException,NumberFormatException{
		try {
		FastScanner sc=new FastScanner();
		int h=sc.nextInt(),w=sc.nextInt();
		if(h%3==0||w%3==0) {
			System.out.println(0);
		}
		else {
			int a=Math.max(h, w);
			int b=Math.min(h, w);
			if(a%2==0&&b%2==0) {
				System.out.println(Math.min(h, w)/2);
				return;
			}
			h=a/2;
		    w=a-h;
		    int max=h*b;
		    b=b/2;
		    int min=b*w;
		    System.out.println(max+" "+min);
		    System.out.println(max-min);
		    
		    
		}
		}
		catch(Exception e) {
			return ;
		}
		
	}
	static final Random random=new Random();
	
	static void ruffleSort(int[] a) {
		int n=a.length;
		for(int i=0;i<n;i++) {
			int oi=random.nextInt(n),temp=a[oi];
			a[oi]=a[i]; a[i]=temp;
		}
		Arrays.sort(a);
	}
	
	public static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try { 
                                      st=new StringTokenizer(br.readLine());				               
                              } catch (IOException e) {}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
		long[] readLongArray(int n) {
			long[] a=new long[n];
			for(int i=0; i<n ; i++) a[i]=nextLong();
			return a;
		}
		
		String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
	}

}