Every night, the light show "A Symphony of Lights" takes place across the Victoria Harbour. Lights of various colours and types on the skyscrapers are turned on in synchronization with orchestral music. In this problem, you are required to solve a challenge related to the light show!
A Symphony of Lights (© Calvin Sit) Let's say there are $$$N$$$ skyscrapers located on one side of the Victoria Harbour. We index the skyscrapers by $$$1, 2, \dots, N$$$ as viewed from left to right.
For simplicity, suppose the process of "A Symphony of Lights" is as follows:
- At time $$$1$$$, the lights on one skyscraper are turned on.
- Then, at each time $$$i$$$ where $$$2 \leq i \leq N$$$, lights on one more skyscraper are turned on. For the sake of harmony, that skyscraper must be adjacent to some skyscrapers already with lights on.
- Once the lights of a skyscraper are turned on, they remain on until the end of the light show.
- After time $$$N$$$, lights on all the skyscrapers are on.
Your friend told you that at time $$$X$$$, the lights of skyscraper $$$Y$$$ were turned on. Can you find a sequence of turning on the lights of the skyscrapers that matches this information, or report that this is impossible?
Note that if there exist multiple sequences of turning on the lights that are consistent with the given information, you may output any of them.
The first and only line contains three integers: $$$N, X, Y$$$ ($$$1 \leq N \leq 2 \times 10^5$$$, $$$1 \leq X, Y \leq N$$$), the number of skyscrapers, the time of the information, and the index of the skyscraper of the information, respectively.
If it is possible that the target skyscraper appears on at time $$$X$$$, output Yes on the first line. Then, on the second line, output $$$N$$$ integers, the indices of the skyscrapers whose lights are turned on, in chronological order.
Otherwise, output No on the first and only line.
5 2 4
Yes 3 4 2 1 5
5 5 4
No
Sample 1:
Note that the order 5 4 3 2 1 is also accepted.
