Median Pyramid Easy

AtCoder

IDagc006_b

Time2000ms

Memory256MB

Difficulty—

We have a pyramid with $N$ steps, built with blocks. The steps are numbered $1$ through $N$ from top to bottom. For each $1≤i≤N$, step $i$ consists of $2i-1$ blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically. ![image](https://atcoder.jp/img/agc006/a2bde72df5ad036d1699f4a74d74a370.png)A pyramid with $N=4$ steps Snuke wrote a permutation of ($1$, $2$, $...$, $2N-1$) into the blocks of step $N$. Then, he wrote integers into all remaining blocks, under the following rule: * The integer written into a block $b$ must be equal to the median of the three integers written into the three blocks directly under $b$, or to the lower left or lower right of $b$. ![image](https://atcoder.jp/img/agc006/a940f1d8303f255e1f91d17a5696633f.png)Writing integers into the blocks Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step $1$ was $x$. Construct a permutation of ($1$, $2$, $...$, $2N-1$) that could have been written into the blocks of step $N$, or declare that Snuke's memory is incorrect and such a permutation does not exist. ## Constraints * $2≤N≤10^5$ * $1≤x≤2N-1$ ## Input The input is given from Standard Input in the following format: $N$ $x$ [samples]

Samples

Input #1

4 4

Output #1

Yes
1
6
3
7
4
5
2

This case corresponds to the figure in the problem statement.

Input #2

2 1

Output #2

No

No matter what permutation was written into the blocks of step $N$, the integer written into the block of step $1$ would be $2$.

API Response (JSON)

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    "name": "Median Pyramid Easy",
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    "limit": {
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    "difficulty": "None",
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    "sync_url": null,
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    {
      "statement_type": "Markdown",
      "content": "We have a pyramid with $N$ steps, built with blocks. The steps are numbered $1$ through $N$ from top to bottom. For each $1≤i≤N$, step $i$ consists of $2i-1$ blocks aligned horizontally. The pyramid i...",
      "is_translate": false,
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