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: Wrong Answer)

#include <bits//stdc++.h>
using namespace std;
typedef long long ll;
int main() {
	ll ans=99999999999,h,w;
	cin>>h>>w;
	if(h%3==0||w%3==0)
		ans=0;
	if(w==2){
		ans=min(ans,abs(h-(ll)floor((h/2.0))));
	}
	if(h==2){
		ans=min(ans,abs(w-(ll)floor((w/2.0))));
	}
	if(w%3==1){
		ll a=(w-1)/3;
		if(h%2==0){
			ans=min(ans,abs(a*h-(w-a)*h/2));
		}
		else{
			ans=min(ans,abs(a*h-(w-a)*(h-1)/2));
		}
		a=(w+2)/2;
		if(h%2==0){
			ans=min(ans,abs(a*h-(w-a)*h/2));
		}
		else{
			ans=min(ans,abs(a*h-(w-a)*(h-1)/2));
		}
	}
	if(w%3==2){
		ll a=(w-2)/3;
		if(h%2==0){
			ans=min(ans,abs(a*h-(w-a)*h/2));
		}
		else{
			ans=min(ans,abs(a*h-(w-a)*(h-1)/2));
		}
		a=(w+1)/2;
		if(h%2==0){
			ans=min(ans,abs(a*h-(w-a)*h/2));
		}
		else{
			ans=min(ans,abs(a*h-(w-a)*(h-1)/2));
		}
	}
	if(h%3==1){
		ll a=(h-1)/3;
		if(w%2==0){
			ans=min(ans,abs(a*w-(h-a)*w/2));
		}
		else{
			ans=min(ans,abs(a*w-(h-a)*(w-1)/2));
		}
		a=(h+2)/2;
		if(w%2==0){
			ans=min(ans,abs(a*w-(h-a)*w/2));
		}
		else{
			ans=min(ans,abs(a*w-(h-a)*(w-1)/2));
		}
	}
	if(h%3==2){
		ll a=(h-2)/3;
		if(w%2==0){
			ans=min(ans,abs(a*w-(h-a)*w/2));
		}
		else{
			ans=min(ans,abs(a*w-(h-a)*(w-1)/2));
		}
		a=(h+1)/2;
		if(w%2==0){
			ans=min(ans,abs(a*w-(h-a)*w/2));
		}
		else{
			ans=min(ans,abs(a*w-(h-a)*(w-1)/2));
		}
	}
	cout<<ans<<endl;
	return 0;
}