ABS Permutation (Count ver.)

AtCoder

IDarc140_f

Time8000ms

Memory256MB

Difficulty—

Find the number of permutations $P=(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$ that satisfy the following, modulo $998244353$, for each $K=0,1,2,\dots,N-1$. * There are exactly $K$ integers $i$ such that $1 \le i \le N-1$ and $|P_i - P_{i+1}|=M$. ## Constraints * $2 \le N \le 250000$ * $1 \le M \le N-1$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

3 1

Output #1

0 4 2 

*   For $K=0$, the condition is satisfied by no permutations $P$.
*   For $K=1$, the condition is satisfied by four permutations $P$: $(1,3,2),(2,1,3),(2,3,1),(3,1,2)$.
*   For $K=2$, the condition is satisfied by two permutations $P$: $(1,2,3),(3,2,1)$.

Input #2

4 3

Output #2

12 12 0 0

Input #3

10 5

Output #3

1263360 1401600 710400 211200 38400 3840 0 0 0 0

API Response (JSON)

{
  "problem": {
    "name": "ABS Permutation (Count ver.)",
    "description": {
      "content": "Find the number of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ that satisfy the following, modulo $998244353$, for each $K=0,1,2,\\dots,N-1$. *   There are exactly $K$ integers $i$ such th",
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    "platform": "AtCoder",
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number of permutations $P=(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$ that satisfy the following, modulo $998244353$, for each $K=0,1,2,\\dots,N-1$.\n\n*   There are exactly $K$ integers $i$ such th...",
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