D. Multiples and Power Differencestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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).OutputThe output should contain n lines each containing m integers. The j-th integer in the i-th line should be b_{i,j}.ExamplesInput
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
NoteIn 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. 
2 2
1 2
2 3

1 2 2 3 
['constructive algorithms', 'graphs', 'math', 'number theory', '*2200']