Gift for Anton#11815

Gift for Anton

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256 megabytes

Hard

Anton wants to receive as a gift a rectangular table of size $n \times m$ n\times m filled with the numbers $0$ , $1$ , $2$ , $3$ , or $4$ .

Anton will be happy if there is no other $0$ next to each $0$ , exactly one other $1$ next to each $1$ , exactly two other $2$ s next to each $2$ , exactly three other $3$ s next to each $3$ , and exactly four other $4$ s next to each $4$ (i.e., all neighbors of $4$ must also be $4$ ).

One cell is considered to be next to another if they share a side.

You need to come up with a table that can be gifted to Anton so that he will be happy.

Below is an example of a table that will make Anton happy with $n = 4, m = 6$ n=4, m=6.

Input

A single line contains two numbers $n, m$ ( $1 \leq n, m \leq 200$ 1 \leq n, m \leq 200) — the dimensions of the table.

It can be shown that a solution always exists.

Output

Output a table with $n$ rows and $m$ columns — a gift for Anton.

Examples

Example 1

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Scoring

( $10$ points): $n = 1$ n = 1;
( $10$ points): $n = 2$ n = 2;
( $10$ points): $n = 3$ n = 3;
( $10$ points): $n = m = 4$ n = m = 4;
( $10$ points): $n = m = 30$ n = m = 30;
( $5$ points): $n = 30, m = 31$ n = 30, m = 31;
( $5$ points): $n = 30, m = 32$ n = 30, m = 32;
( $10$ points): $n = m = 31$ n = m = 31;
( $5$ points): $n = 31, m = 32$ n = 31, m = 32;
( $10$ points): $n = m = 32$ n = m = 32;
( $15$ points): no additional restrictions.

n \times m

n = 4, m = 6

1 \leq n, m \leq 200

n = 1

n = 2

n = 3

n = m = 4

n = m = 30

n = 30, m = 31

n = 30, m = 32

n = m = 31

n = 31, m = 32

n = m = 32