An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. The examples of arithmetic progressions are as follows:

• $\{ 1, 3, 5, 7 \}$: Difference is $2$
• $\{ 7.53, 4.32, 1.11, -2.1, -5.31 \}$: Difference is $-3.21$ 

Whereas, $\{ 1, 2, 1 \}$ is not an arithmetic progression.

A subsequence of sequence $A$ is a sequence that is obtained from $A$ by removing several (zero or more) elements from it. For example, $\{ 1, 3, 4 \}$, $\{ 1, 2, 3, 4, 5 \}$, and $\{ \}$ (empty sequence) are the subsequences of $\{ 1, 2, 3, 4, 5 \}$.

An arithmetic subsequence of sequence $A$ is a subsequence of $A$, that is an arithmetic progression. You are given integers $n$ and $k$. Your task is to construct any permutation of first $n$ positive integers such that the length of the longest arithmetic subsequence of the permutation is equal to $k$ or determine that there is no such permutation at all.

Input format

The first and only line of input contains two integers $n$ and $k$ denoting the length of the required permutation and the length of the longest arithmetic subsequence of the required permutation respectively.

Output format

If there no such permutations exist, then print $No$ in a single line. If such permutations exist, then print $Yes$ in the first line and the constructed permutation in the second line. The permutation must contain each integer from $1$ to $n$ (both inclusive) exactly once. The elements must be space-separated. If there are several possible permutations, then you can output any of them.

Constraints

$1 \le k \le n \le 5000$