Between B and B

AtCoder

IDarc179_b

Time2000ms

Memory256MB

Difficulty—

You are given a sequence $(X_1, X_2, \dots, X_M)$ of length $M$ consisting of integers between $1$ and $M$, inclusive. Find the number, modulo $998244353$, of sequences $A = (A_1, A_2, \dots, A_N)$ of length $N$ consisting of integers between $1$ and $M$, inclusive, that satisfy the following condition: * For each $B = 1, 2, \dots, M$, the value $X_B$ exists between any two different occurrences of $B$ in $A$ (including both ends). More formally, for each $B = 1, 2, \dots, M$, the following condition must hold: * For every pair of integers $(l, r)$ such that $1 \leq l < r \leq N$ and $A_l = A_r = B$, there exists an integer $m$ ($l \leq m \leq r$) such that $A_m = X_B$. ## Constraints * $1 \leq M \leq 10$ * $1 \leq N \leq 10^4$ * $1 \leq X_i \leq M$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $M$ $N$ $X_1$ $X_2$ $\cdots$ $X_M$ [samples]

Samples

Input #1

3 4
2 1 2

Output #1

14

Here are examples of sequences $A$ that satisfy the condition:

*   $(1, 3, 2, 3)$
*   $(2, 1, 2, 1)$
*   $(3, 2, 1, 3)$

Here are non-examples:

*   $(1, 3, 1, 3)$
    *   There is no $X_3 = 2$ between the $3$s.
*   $(2, 2, 1, 3)$
    *   There is no $X_2 = 1$ between the $2$s.

Input #2

4 8
1 2 3 4

Output #2

65536

All sequences of length $8$ consisting of integers between $1$ and $4$ satisfy the condition.
Note that when $X_B = B$, there is always a $B$ between two different occurrences of $B$.

Input #3

4 9
2 3 4 1

Output #3

API Response (JSON)

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    "name": "Between B and B",
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      "content": "You are given a sequence $(X_1, X_2, \\dots, X_M)$ of length $M$ consisting of integers between $1$ and $M$, inclusive. Find the number, modulo $998244353$, of sequences $A = (A_1, A_2, \\dots, A_N)$ of",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc179_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence $(X_1, X_2, \\dots, X_M)$ of length $M$ consisting of integers between $1$ and $M$, inclusive.\nFind the number, modulo $998244353$, of sequences $A = (A_1, A_2, \\dots, A_N)$ of...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments