9100: CCC '23 S3 - Palindromic Poster
[Creator : ]
Description
Ryo and Kita are designing a new poster for Kessoku Band. After some furious brainstorming, they came to the conclusion that the poster should come in the form of a 2-D grid of lowercase English letters (i.e. a to z), with $N$ rows and $M$ columns.
Furthermore, it is known that Ryo and Kita both have peculiar tastes in palindromes. Ryo will only be satisfied with the poster if exactly $R$ of its rows are palindromes, and Kita will only be satisfied with the poster if exactly $C$ of its columns are palindromes. Can you design a poster that will satisfy both Ryo and Kita, or determine that it is impossible to do so?
Note: A string is considered a palindrome if it is the same when read forwards and backwards. For example, kayak and bb are palindromes, whereas guitar and live are not.
Furthermore, it is known that Ryo and Kita both have peculiar tastes in palindromes. Ryo will only be satisfied with the poster if exactly $R$ of its rows are palindromes, and Kita will only be satisfied with the poster if exactly $C$ of its columns are palindromes. Can you design a poster that will satisfy both Ryo and Kita, or determine that it is impossible to do so?
Note: A string is considered a palindrome if it is the same when read forwards and backwards. For example, kayak and bb are palindromes, whereas guitar and live are not.
Input
The first and only line of input consists of 4 space-separated integers $N,M,R,C$.
Output
If it is impossible to design a poster that will satisfy both Ryo and Kita, output IMPOSSIBLE on a single line.
Otherwise, your output should contain $N$ lines, each consisting of $M$ lowercase English letters, representing your poster design.
If there are multiple possible designs, output any of them.
Otherwise, your output should contain $N$ lines, each consisting of $M$ lowercase English letters, representing your poster design.
If there are multiple possible designs, output any of them.
Constraints
The following table shows how the available 15 marks are distributed:
| Marks Awarded | Bounds on N | Bounds on M | Bounds on R | Bounds on C |
|---|---|---|---|---|
| 2 marks | 2≤N≤2000 | 2≤M≤2000 | R=1 | C=1 |
| 2 marks | N=2 | M=2 | 0≤R≤N | 0≤C≤M |
| 4 marks | N=2 | 2≤M≤2000 | 0≤R≤N | 0≤C≤M |
| 7 marks | 2≤N≤2000 | 2≤M≤2000 | 0≤R≤N | 0≤C≤M |
Sample 1 Input
4 5 1 2
Sample 1 Output
union
radar
badge
anime
In the given design, only the second row (namely radar) and the second and third columns (namely naan and iddi) are palindromes. Since exactly R=1 of the rows and C=2 of the columns are palindromes, this is an acceptable design.
Sample 2 Input
2 2 2 1
Sample 2 Output
IMPOSSIBLE