[CCC 2023 S3] Palindromic Poster

Luogu

IDLGP9326

Time1000ms

Memory512MB

DifficultyP4

模拟字符串2023Special JudgeCCC（加拿大）构造分类讨论

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 $2\text{-D}$ 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. ## Input The first and only line of input consists of $4$ space-separated integers $N, M, R$, and $C$. The following table shows how the available $15$ marks are distributed. | Marks | Bounds on $N$ | Bounds on $M$ | Bounds on $R$ | Bounds on $C$ | | :-----------: | :-----------: | :-----------: | :-----------: | :-----------: | | $2$ marks | $2 \leq N \leq 2000$ | $2 \leq M \leq 2000$ | $R = 1$ | $C = 1$ | | $2$ marks | $N = 2$ | $M = 2$ | $0 \leq R \leq N$ | $0 \leq C \leq M$ | | $4$ marks | $N = 2$ | $2 \leq M \leq 2000$ | $0 \leq R \leq N$ | $0 \leq C \leq M$ | | $7$ marks | $2 \leq N \leq 2000$ | $2 \leq M \leq 2000$ | $0 \leq R \leq N$ | $0 \leq C \leq M$ | ## 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 ofthem. [samples] ## Note Explanation of Output for Sample Input $1$： 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. Explanation of Output for Sample Input $2$： In this case, it can be proven that it is impossible to satisfy both Ryo and Kita. **本题采用捆绑测试**： - Subtask 1（2 points）：数据保证 $2 \leq N \leq 2000$，$2\leq M\leq 2000$，$R = 1$，$C = 1$。 - Subtask 2（2 points）：数据保证 $N = 2$，$M = 2$，$0\leq R\leq N$，$0\leq C\leq M$。 - Subtask 3（4 points）：数据保证 $N = 2$，$2\leq M \leq2000$，$0\leq R\leq N$，$0\leq C\leq M$。 - Subtask 4（7 points）：数据保证 $2\leq N\leq 2000$，$2\leq M \leq2000$，$0\leq R\leq N$，$0\leq C\leq M$。

Samples

Input #1

4 5 1 2

Output #1

union
radar
badge
anime

Input #2

2 2 2 1

Output #2

IMPOSSIBLE

API Response (JSON)

{
  "problem": {
    "name": "[CCC 2023 S3] Palindromic Poster",
    "description": {
      "content": "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 $2\\text{-D}$ grid of lowercase Engl",
      "description_type": "Markdown"
    },
    "platform": "Luogu",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 524288
    },
    "difficulty": {
      "LuoguStyle": "P4"
    },
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "LGP9326"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 $2\\text{-D}$ grid of lowercase Engl...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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