Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

J. Planting Trees

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasya 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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/21/2019 14:18:56 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|