Multiples and Power Differences (Codeforces 1485D)
Tags: Math, number theory

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

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

Sample Inputs:
2 2
1 2
2 3

2 3
16 16 16
16 16 16

2 2
3 11
12 8

Sample Outputs:
1 2
2 3

16 32 48
32 48 64

327 583
408 664

Solution (Python):
(n, m) = map(int, input().split())
a = []
for i in range(n):
    a.append(list(map(int, input().split())))
lcm = 720720
for i in range(n):
    line = []
    for j in range(m):
        if (i + j) % 2 == 0:
            line.append('%d' % (lcm + a[i][j] ** 4))
        else:
            line.append('%d' % lcm)
    print(' '.join(line))

Solution (Python):
(n, m) = map(int, input().split())
arr = [[int(num) for num in input().split()] for _ in range(n)]
lcm = 720720
for i in range(n):
    line = []
    for j in range(m):
        if (i + j) % 2 == 0:
            line.append(str(lcm + arr[i][j] ** 4))
        else:
            line.append(str(lcm))
    print(' '.join(line))

Solution (Python):
(n, m) = tuple([int(x) for x in input().split()])
aa = []
for i in range(n):
    aa.append([int(x) for x in input().split()])
bb = []
for i in range(n):
    bb.append([720720 for i in range(m)])
for i in range(n):
    for j in range(m):
        if (i + j) % 2 == 1:
            bb[i][j] += aa[i][j] ** 4
for i in range(n):
    print(' '.join([str(x) for x in bb[i]]))