#P1485D. Multiples and Power Differences
Multiples and Power Differences
Description
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 $b_{i,j}$.
Input
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 $a_{i,j}$ ($1 \le a_{i,j} \le 16$).
Output
The output should contain $n$ lines each containing $m$ integers. The $j$-th integer in the $i$-th line should be $b_{i,j}$.
Samples
2 2
1 2
2 3
1 2
2 3
2 3
16 16 16
16 16 16
16 32 48
32 48 64
2 2
3 11
12 8
327 583
408 664
Note
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 $8$;
- $|408 - 327| = 3^4$, $|583 - 327| = 4^4$, $|664 - 408| = 4^4$, $|664 - 583| = 3^4$.