Perfect Strings

AtCoder

IDagc061_f

Time10000ms

Memory256MB

Difficulty—

There are positive integers $N$ and $M$. A binary string $s$ is called **good** if all of the followings are satisfied: * $s$ is non-empty. * The number of `1`s in $s$ is a multiple of $N$. * The number of `0`s in $s$ is a multiple of $M$. A good string is called **perfect** if it doesn't contain shorter good (contiguous) substrings. For example, if $N = 3$ and $M = 2$, then strings `111`, `00` and `10101` are perfect, but `0000` and `11001` are not. One can show that for any $N, M$ the number of perfect strings is finite. Find this number modulo $998\,244\,353$. ## Constraints * $1 \leq N, M \leq 40$ * All values in the input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 2

Output #1

4

The perfect strings are `00`, `0101`, `1010`, `11`.

Input #2

3 2

Output #2

7

The perfect strings are `00`, `01011`, `01101`, `10101`, `10110`, `11010`, `111`.

Input #3

23 35

Output #3

212685109

API Response (JSON)

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    "name": "Perfect Strings",
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      "content": "There are positive integers $N$ and $M$. A binary string $s$ is called **good** if all of the followings are satisfied: *   $s$ is non-empty. *   The number of `1`s in $s$ is a multiple of $N$. *   T",
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    "sign": "agc061_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are positive integers $N$ and $M$.\nA binary string $s$ is called **good** if all of the followings are satisfied:\n\n*   $s$ is non-empty.\n*   The number of `1`s in $s$ is a multiple of $N$.\n*   T...",
      "is_translate": false,
      "language": "English"
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