Problem: Vasya is a Greencode wildlife preservation society proponent. One day he found an empty field nobody owned, divided it into n × m squares and decided to plant a forest there. Vasya will plant nm trees of all different heights from 1 to nm. For his forest to look more natural he wants any two trees growing in the side neighbouring squares to have the absolute value of difference in heights to be strictly more than 1. Help Vasya: make the plan of the forest planting for which this condition is fulfilled.

Input

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 100) — the number of rows and columns on Vasya's field

Output

If there's no solution, print -1. Otherwise, print n lines containing m numbers each — the trees' planting plan. In every square of the plan the height of a tree that should be planted on this square should be written. If there are several solutions to that problem, print any of them.

Examples

Input

2 3


Output

3 6 2
5 1 4


Input

2 1


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

public class J implements Runnable {
	public static void main(String[] args) {
		new J().run();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		boolean eof;
		String buf;

		public FastScanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
			nextToken();
		}

		public FastScanner(InputStream stream) {
			br = new BufferedReader(new InputStreamReader(stream));
			nextToken();
		}

		String nextToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					eof = true;
					break;
				}
			}
			String ret = buf;
			buf = eof ? "-1" : st.nextToken();
			return ret;
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}

		BigInteger nextBigInteger() {
			return new BigInteger(nextToken());
		}

		void close() {
			try {
				br.close();
			} catch (Exception e) {

			}
		}

		boolean isEOF() {
			return eof;
		}
	}

	FastScanner sc;
	PrintWriter out;

	public void run() {
		Locale.setDefault(Locale.US);
		try {
			sc = new FastScanner(System.in);
			out = new PrintWriter(System.out);
			solve();
			sc.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	int nextInt() {
		return sc.nextInt();
	}

	String nextToken() {
		return sc.nextToken();
	}

	long nextLong() {
		return sc.nextLong();
	}

	double nextDouble() {
		return sc.nextDouble();
	}

	BigInteger nextBigInteger() {
		return sc.nextBigInteger();
	}

	void solve() {
		int n = nextInt();
		int m = nextInt();
		if (n == 1 && m == 1) {
			out.println(1);
			return;
		}
		if (n <= 2 && m <= 2 || (n == 1 && m == 3) || (n == 3 && m == 1)) {
			out.println(-1);
			return;
		}
		int iter = 100000 / n / m;
		loop: for (int it = 0; it < iter; it++) {
			TreeSet<Integer> ts = new TreeSet<Integer>();
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					ts.add(i * m + j);
				}
			}
			int[][] ans = new int[n][m];
			for (int i = 0; i < ans.length; i++) {
				Arrays.fill(ans[i], -5);
			}
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					Integer e;
					int cnt = 0;
					do {
						e = rand.nextBoolean() ? ts
								.ceiling(rand.nextInt(n * m)) : ts.floor(rand
								.nextInt(n * m));
						++cnt;
						if (e != null) {
							ans[i][j] = e;
						}
					} while (cnt < 105 && (e == null || !check(ans, i, j)));
					if (cnt == 105) {
						continue loop;
					}
					ts.remove(e);
					ans[i][j] = e;
				}
			}
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					if (!check(ans, i, j)) {
						continue loop;
					}
				}
			}
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					out.print(1 + ans[i][j] + " ");
				}
				out.println();
			}
			return;
		}		
	}

	final int[] DX = { 1, 0, -1, 0 };
	final int[] DY = { 0, 1, 0, -1 };

	boolean check(int[][] a, int x, int y) {
		for (int dir = 0; dir < 4; dir++) {
			int xx = x + DX[dir];
			int yy = y + DY[dir];
			if (xx < 0 || yy < 0 || xx >= a.length || yy >= a[xx].length) {
				continue;
			}
			if (Math.abs(a[xx][yy] - a[x][y]) <= 1) {
				return false;
			}
		}
		return true;
	}

	final Random rand = new Random(this.hashCode());
}