A14140. Multiples and Power Differences

You are given a matrix $a$ consisting of positive integers. It has $n$ rows and $m$ columns.

Construct a matrix $b$ consisting of positive integers. It should have the same size as $a$ , and the following conditions should be met:

- $1 \le b_{i,j} \le 10^6$ ;
- $b_{i,j}$ is a multiple of $a_{i,j}$ ;
- the absolute value of the difference between numbers in any adjacent pair of cells (two cells that share the same side) in $b$ is equal to $k^4$ for some integer $k \ge 1$ ( $k$ is not necessarily the same for all pairs, it is own for each pair).

We can show that the answer always exists.

The first line contains two integers $n$ and $m$ ( $2 \le n,m \le 500$ ).

Each of the following $n$ lines contains $m$ integers. The $j$ -th integer in the $i$ -th line is $a_{i,j}$ ( $1 \le a_{i,j} \le 16$ ).

The output should contain $n$ lines each containing $m$ integers. The $j$ -th integer in the $i$ -th line should be $b_{i,j}$ .

In the first example, the matrix $a$ can be used as the matrix $b$ , because the absolute value of the difference between numbers in any adjacent pair of cells is $1 = 1^4$ .

In the third example:

- $327$ is a multiple of $3$ , $583$ is a multiple of $11$ , $408$ is a multiple of $12$ , $664$ is a multiple of $8$ ;
- $|408 - 327| = 3^4$ , $|583 - 327| = 4^4$ , $|664 - 408| = 4^4$ , $|664 - 583| = 3^4$ .