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.util.*;
import java.io.*;
import java.math.*;
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int t = 1;
        Task solver = new Task();
        while ((t --) > 0)
            solver.solve(in, out);
        out.close();
    }
}
class Task{
    void solve (InputReader cin , PrintWriter cout) {
        int n = cin.nextInt() , m = cin.nextInt();
        if (n == 1 && m == 1) {
            cout.println(1);
            return ;
        }
        if (n + m <= 4) {
            cout.println(-1);
            return ;
        }
        if (n == 1) {
            for (int i = 1 , j = m / 2 + 1 , k = 1 ; i <= m ; i ++) {
                if (i % 2 == 1) {
                    cout.print(j + " ");
                    j ++;
                }
                else {
                    cout.print(k + " ");
                    k ++;
                }
            }
            cout.println();
            return ;
        }
        if (m == 1) {
            for (int i = 1 , j = n / 2 + 1 , k = 1 ; i <= n ; i ++) {
                if (i % 2 == 1) {
                    cout.println(j);
                    j ++;
                }
                else {
                    cout.println(k);
                    k ++;
                }
            }
            return ;
        }
        int a[][] = new int [105][105];
        int b[][] = new int [105][105];
        for (int i = 0 ; i < n ; i ++) {
            int k = i + 1;
            for (int j = 0 ; j < m ; j ++ , k += n) {
                a[i][j] = k;
            }
        }
        for (int i = 0 ; i < n ; i ++) {
            for (int j = 0 ; j < m ; j ++) {
                b[i][j] = a[i][(j + i) % m];
            }
        }
        for (int i = 0 ; i < n ; i ++) {
            for (int j = 0 ; j < m ; j ++)
                cout.print(b[i][j] + " ");
            cout.println();
        }
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
}