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: Wrong Answer)

import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int H = sc.nextInt();
		int W = sc.nextInt();
		if (H % 3 == 0 || W % 3 == 0) {
			System.out.println(0);
		} else {
			if (W > H) {
				int w1 = (int) Math.ceil(W / 3.0);
				int[] size1 = {
						w1 * H,
						(W - w1) * (H / 2),
						(W - w1) * (H - (H / 2))
				};
				int diff1 = max(size1) - min(size1);

				int w2 = (int) Math.floor(W / 3.0);
				int[] size2 = {
						w2 * H,
						(W - w2) * (H / 2),
						(W - w2) * (H - (H / 2))
				};
				int diff2 = max(size2) - min(size2);

				System.out.println(Math.min(diff1, diff2));
			} else {
				int h1 = (int) Math.ceil(H / 3.0);
				int[] size1 = {
						h1 * W,
						(H - h1) * (W / 2),
						(H - h1) * (W - (W / 2))
				};
				int diff1 = max(size1) - min(size1);

				int h2 = (int) Math.floor(H / 3.0);
				int[] size2 = {
						h2 * W,
						(H - h2) * (W / 2),
						(H - h2) * (W - (W / 2))
				};
				int diff2 = max(size2) - min(size2);

				System.out.println(Math.min(diff1, diff2));
			}
		}
	}

	private static int min(int... values) {
		Arrays.sort(values);
		return values[0];
	}

	private static int max(int... values) {
		Arrays.sort(values);
		return values[values.length - 1];
	}

	public static class Pair {
		private int key;
		private int value;

		public Pair(int key, int value) {
			super();
			this.key = key;
			this.value = value;
		}

		public int getKey() {
			return key;
		}

		public int getValue() {
			return value;
		}

		public void setValue(int value) {
			this.value = value;
		}

		@Override
		public String toString() {
			return "{" + key + ", " + value + "}";
		}
	}

	private static boolean isDebug = System.getProperty("sun.desktop") != null;

	private static void debug(Object... o) {
		if (isDebug) {
			System.err.println(Arrays.deepToString(o));
		}
	}

	public static class Scanner {
		private BufferedInputStream inputStream;

		public Scanner(InputStream in) {
			inputStream = new BufferedInputStream(in);
		}

		public int nextInt() throws IOException {
			int num = 0;
			int sign = 1;

			int read = skip();
			if (read == '-') {
				sign = -1;
				read = inputStream.read();
			}

			do {
				num = num * 10 + sign * (read - 0x30);
			} while ((read = inputStream.read()) > 0x20);

			return num;
		}

		public void fill(int[] a) throws IOException {
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
		}

		public void fill(int[] a, int[] b) throws IOException {
			if (a.length != b.length) {
				throw new IllegalArgumentException();
			}

			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
				b[i] = nextInt();
			}
		}

		public void fill(int[] a, int[] b, int[] c) throws IOException {
			if (a.length != b.length || b.length != c.length) {
				throw new IllegalArgumentException();
			}

			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
				b[i] = nextInt();
				c[i] = nextInt();
			}
		}

		public long nextLong() throws IOException {
			long num = 0;

			int read = skip();
			do {
				num = num * 10 + (read - 0x30);
			} while ((read = inputStream.read()) > 0x20);

			return num;
		}

		public void fill(long[] a) throws IOException {
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
		}

		public void fill(long[] a, long[] b) throws IOException {
			if (a.length != b.length) {
				throw new IllegalArgumentException();
			}

			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
				b[i] = nextLong();
			}
		}

		public long[] nextLong(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++) {
				array[i] = nextLong();
			}

			return array;
		}

		public String next() throws IOException {
			StringBuilder builder = new StringBuilder();

			int read = skip();
			do {
				builder.append((char) read);
			} while ((read = inputStream.read()) > 0x20);

			return builder.toString();
		}

		private int skip() throws IOException {
			int read;
			while ((read = inputStream.read()) <= 0x20)
				;

			return read;
		}
	}
}