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 <iostream>
#include <algorithm>
#include <cmath>
using namespace std;
int main() {
	int n,m;
	cin>>n>>m;
	if(n%3==0&&m!=n/3){
		cout<<"0"<<endl;
	}
	else if(m%3==0&&n!=m/3){
		cout<<"0"<<endl;
	}
	else if(m%2==0&&n%2==0){
		cout<<min(m,n)/2<<endl;
	}
	else{
		//case 1
		int max1;
		if(m%3!=0){
			max1=n;
		}
		//case 2
		int max2;
		if(n%3!=0){
			max2=m;
		}
		//case 3 4 
		double maxs,mins;
		double step1up,step1down;
		step1up=(double)ceil((double)max(m,n)/2);
		step1down=(double)floor((double)max(m,n)/2);
		maxs=step1down*min(m,n);
		double step2up,step2down;
		if((int)step1up%2!=0){
			step2up=(double)ceil((double)max(m,n)/2);
			step2down=(double)floor((double)max(m,n)/2);
			mins=step2down*(m-step1down);
		}
		if((int)step1up%2==0){
			mins=(max(m,n)/2)*(m-step1down);
		}
	int areukidingme[3]={max1,max2,(int)maxs-(int)mins};
	sort(areukidingme+0,areukidingme+3);
	cout<<areukidingme[0];
	}
	return 0;
}