Multiples and Power Differences

题意翻译

有一个矩阵 $a$ ,请你构造一个矩阵 $b$ ，使得： - $0<b_{i,j}\le 10^6$ - $b_{i,j}$ 是 $a_{i,j}$ 的倍数 - $b$ 中相邻的两个数的差的绝对值可以写成 $k^4(k\in\mathbb{N}^+)$ $1\le a_{i,j}\le 16$ 翻译 by jun头吉吉

题目描述

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.

输入输出格式

输入格式

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 $ ).

输出格式

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

输入输出样例

输入样例 #1

2 2
1 2
2 3

输出样例 #1

1 2
2 3

输入样例 #2

2 3
16 16 16
16 16 16

输出样例 #2

16 32 48
32 48 64

输入样例 #3

2 2
3 11
12 8

输出样例 #3

327 583
408 664

说明

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 $ .