Differ by K bits

AtCoder

IDarc138_d

Time2000ms

Memory256MB

Difficulty—

You are given integers $N$ and $K$. Determine whether there exists a permutation $P=(P_0,P_1,\cdots,P_{2^N-1})$ of $(0,1,\cdots,2^N-1)$ satisfying the condition below, and construct one such sequence if it exists. Note that $P$ is $0$\-indexed. * For every $i$ ($0 \leq i \leq 2^N-1$), $P_i$ and $P_{i+1 \mod 2^N}$ differ by exactly $K$ bits in binary representation. The comparison is made after zero-padding both integers to $N$ bits. ## Constraints * $1 \leq K \leq N \leq 18$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

3 1

Output #1

Yes
0 1 3 2 6 7 5 4

Here, we have $P=(000,001,011,010,110,111,101,100)$ in binary representation.
We can see that $P_1=001$ and $P_2=011$, for example, differ by exactly $1$ bit, satisfying the condition for $i=1$. The same goes for every $i$.

Input #2

2 2

Output #2

No

API Response (JSON)

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    "name": "Differ by K bits",
    "description": {
      "content": "You are given integers $N$ and $K$. Determine whether there exists a permutation $P=(P_0,P_1,\\cdots,P_{2^N-1})$ of $(0,1,\\cdots,2^N-1)$ satisfying the condition below, and construct one such sequence ",
      "description_type": "Markdown"
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    "platform": "AtCoder",
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      "time_limit": 2000,
      "memory_limit": 262144
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    "sign": "arc138_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integers $N$ and $K$. Determine whether there exists a permutation $P=(P_0,P_1,\\cdots,P_{2^N-1})$ of $(0,1,\\cdots,2^N-1)$ satisfying the condition below, and construct one such sequence ...",
      "is_translate": false,
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