Finite Encyclopedia of Integer Sequences

AtCoder

IDarc084_c

Time2000ms

Memory256MB

Difficulty—

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between $1$ and $N$ (inclusive) consisting of integers between $1$ and $K$ (inclusive) are listed. Let the total number of sequences listed in FEIS be $X$. Among those sequences, find the $(X/2)$\-th (rounded up to the nearest integer) lexicographically smallest one. ## Constraints * $1 \leq N,K \leq 3 × 10^5$ * $N$ and $K$ are integers. ## Input Input is given from Standard Input in the following format: $K$ $N$ [samples]

Samples

Input #1

3 2

Output #1

2 1 

There are $12$ sequences listed in FEIS: $(1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3)$. The $(12/2 = 6)$\-th lexicographically smallest one among them is $(2,1)$.

Input #2

2 4

Output #2

1 2 2 2

Input #3

5 14

Output #3

3 3 3 3 3 3 3 3 3 3 3 3 2 2

API Response (JSON)

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    "name": "Finite Encyclopedia of Integer Sequences",
    "description": {
      "content": "In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between $1$ and $N$ (inclusive) consisting of integers between $1$ and $K$ (inclusive) are listed. Let the total nu",
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      "statement_type": "Markdown",
      "content": "In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between $1$ and $N$ (inclusive) consisting of integers between $1$ and $K$ (inclusive) are listed.\nLet the total nu...",
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