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D. Multiples and Power Differences

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$8$$$;
- $$$|408 - 327| = 3^4$$$, $$$|583 - 327| = 4^4$$$, $$$|664 - 408| = 4^4$$$, $$$|664 - 583| = 3^4$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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