D. Multiples and Power Differences
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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 $$$b_{i,j}$$$.

Examples
Input
2 2
1 2
2 3
Output
1 2
2 3
Input
2 3
16 16 16
16 16 16
Output
16 32 48
32 48 64
Input
2 2
3 11
12 8
Output
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 $$$8$$$;
  • $$$|408 - 327| = 3^4$$$, $$$|583 - 327| = 4^4$$$, $$$|664 - 408| = 4^4$$$, $$$|664 - 583| = 3^4$$$.