Score : 400 points
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.
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:
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.
The input is given from Standard Input in the following format:
N x
If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print No
.
Otherwise, print Yes
in the first line, then print 2N-1 lines in addition.
The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.
4 4
Yes 1 6 3 7 4 5 2
This case corresponds to the figure in the problem statement.
2 1
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.