|{floor(A_i/2^k)}|

AtCoder

IDarc182_b

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $N$ and $K$. An integer sequence of length $N$ where all elements are between $1$ and $2^K - 1$, inclusive, is called a **good sequence**. The **score** of a good sequence $A=(A_1,A_2,\ldots,A_N)$ is defined as follows: * The number of distinct integers that can be expressed as $\displaystyle \left\lfloor\frac{A_i}{2^k} \right\rfloor$ using an integer $i$ between $1$ and $N$, inclusive, and a non-negative integer $k$. For example, for $A=(3,5)$, five integers can be expressed as $\displaystyle \left\lfloor\frac{A_i}{2^k} \right\rfloor$: $0$, $1$, $2$, $3$, and $5$, so the score is $5$. Find one good sequence with the maximum score. For each input file, you are given $T$ test cases to solve. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq N \leq 10^5$ * $1 \leq K \leq 30$ * The sum of $N$ across the test cases in a single input file is at most $2 \times 10^5$. * All input values are integers. ## Input The input is given from Standard Input in the following format. Here, $\text{case}_i$ denotes the $i$\-th test case. $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each test case is given in the following format: $N$ $K$ [samples]

Samples

Input #1

Output #1

5 6 7
2 2 3 3 1 3 3
662933 967505 876482 840117 1035841 651549 543175 781219

Consider the first test case.
For $A=(5,6,7)$, seven integers can be expressed as $\displaystyle \left\lfloor\frac{A_i}{2^k} \right\rfloor$: $0$, $1$, $2$, $3$, $5$, $6$, and $7$, so its score is $7$.
Outputs such as $A=(7,4,5)$ and $A=(6,5,4)$ would also be accepted.

API Response (JSON)

{
  "problem": {
    "name": "|{floor(A_i/2^k)}|",
    "description": {
      "content": "You are given positive integers $N$ and $K$. An integer sequence of length $N$ where all elements are between $1$ and $2^K - 1$, inclusive, is called a **good sequence**. The **score** of a good seque",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given positive integers $N$ and $K$.\nAn integer sequence of length $N$ where all elements are between $1$ and $2^K - 1$, inclusive, is called a **good sequence**.\nThe **score** of a good seque...",
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      "language": "English"
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