Increasing K Times

AtCoder

IDabc267_g

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A = (A_1, \dots, A_N)$ of length $N$. Find the number, modulo $998244353$, of permutations $P = (P_1, \dots, P_N)$ of $(1, 2, \dots, N)$ such that: * there exist exactly $K$ integers $i$ between $1$ and $(N-1)$ (inclusive) such that $A_{P_i} \lt A_{P_{i + 1}}$. ## Constraints * $2 \leq N \leq 5000$ * $0 \leq K \leq N - 1$ * $1 \leq A_i \leq N \, (1 \leq i \leq N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4 2
1 1 2 2

Output #1

4

Four permutations satisfy the condition: $P = (1, 3, 2, 4), (1, 4, 2, 3), (2, 3, 1, 4), (2, 4, 1, 3)$.

Input #2

10 3
3 1 4 1 5 9 2 6 5 3

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Increasing K Times",
    "description": {
      "content": "You are given an integer sequence $A = (A_1, \\dots, A_N)$ of length $N$. Find the number, modulo $998244353$, of permutations $P = (P_1, \\dots, P_N)$ of $(1, 2, \\dots, N)$ such that: *   there exist ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "abc267_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A = (A_1, \\dots, A_N)$ of length $N$.\nFind the number, modulo $998244353$, of permutations $P = (P_1, \\dots, P_N)$ of $(1, 2, \\dots, N)$ such that:\n\n*   there exist ...",
      "is_translate": false,
      "language": "English"
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}

Full JSON Raw Segments