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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std; 
long long s3,s2,s1,ans,x,e,h,w,a,b;
int main(){	
	cin>>h>>w;
	if(h%3==0||w%3==0) {cout<<0;return 0;}
	ans=h*w;
	for(int i=h/3;i<=h/2;i++)
	{   
	    b=h;
	    a=w;
		s1=i*w;
        b-=i;
        a/=2;
	    s2=a*b;
	    s3=h*w-s1-s2;
	    e=min(min(s2,s3),s1);
	    x=max(max(s2,s3),s1);
	    ans=min(x-e,ans);                                                
    	a=w;
	    b/=2;
	    s2=a*b;
	    s3=h*w-s1-s2;
	    e=min(min(s2,s3),s1);
		x=max(max(s2,s3),s1);
	    ans=min(ans,x-e);
	}
	for(int i=w/3;i<=w/2;i++)
	{
	    a=w;
	    b=h;
		s1=i*h;
		a-=i;
		b/=2;
	    s2=a*b;
	    s3=h*w-s1-s2;
	    e=min(min(s2,s3),s1);
	    x=max(max(s2,s3),s1);
	    ans=min(x-e,ans);
	    b=h;
	    a/=2;
	    s2=a*b;
	    s3=h*w-s1-s2;
	    e=min(min(s2,s3),s1);
	    x=max(max(s2,s3),s1);
	    ans=min(ans,x-e);
	}
	cout<<ans;
	return 0;
}