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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)





import java.util.Scanner;

class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

		long H=sc.nextLong();
		long W=sc.nextLong();
		long diff=1000000007;

		long ni_kiriwake=0;

		long tmp1=0,tmp2=0,tmp3=0,tmp4=0;
		if(H%3==0 || W%3==0) {		//どちらかの辺が３の倍数ならば無条件でみんな同じ面積に切り分けることができる
			System.out.println(0);
		}

		else if(H==W) {		//正方形の時
			ni_kiriwake=(H+1)/2;

			for(int i=1; i<W; i++) {
				tmp1=(H-ni_kiriwake)*(W-i);
				tmp2=ni_kiriwake*(W-i);
				tmp3=H*i;
				tmp4=Math.max(tmp1, Math.max(tmp2, tmp3))-Math.min(tmp1, Math.min(tmp2, tmp3));
				diff=Math.min(diff, tmp4);
			}

			if(H>3) {
				diff=Math.min(diff, H);		// 320x320 なら 107　107　106*320　みたいに
			}
			System.out.println(diff);
		}

		else if(H!=W) {
			ni_kiriwake=(H+1)/2;

			for(int i=1; i<W; i++) {
				tmp1=ni_kiriwake*i;
				tmp2=(H-ni_kiriwake)*i;
				tmp3=H*(W-i);
				tmp4=Math.max(tmp1, Math.max(tmp2, tmp3))-Math.min(tmp1, Math.min(tmp2, tmp3));
				diff=Math.min(diff, tmp4);
			}

			if(H>3) {
				diff=Math.min(diff,W);		// 320x320 なら 107　107　106*320　みたいに
			}

			ni_kiriwake=(W+1)/2;

			for(int i=1; i<H; i++) {
				tmp1=ni_kiriwake*i;
				tmp2=(W-ni_kiriwake)*i;
				tmp3=W*(H-i);
				tmp4=Math.max(tmp1, Math.max(tmp2, tmp3))-Math.min(tmp1, Math.min(tmp2, tmp3));
				diff=Math.min(diff, tmp4);
			}

			if(W>3) {
				diff=Math.min(diff,H);		// 320x320 なら 107　107　106*320　みたいに
			}

			System.out.println(diff);
		}
	}
}