$\textrm{MEX}$ is a function that finds the smallest non-negative integer not included in a set. For example, $\textrm{MEX}(\{0,1,3,4\})=2$ and $\textrm{MEX}(\{1,2,4\})=0$.

ibasic defined the $\textrm{MEXMEX}$ function for a sequence $A$ of length $N$ consisting of non-negative integers as follows: $$\textrm{MEXMEX}(A)=\textrm{MEX}(\{\textrm{MEX}(\{A_l,A_{l+1},\dots,A_r\})\mid 1\le l\le r\le N\})$$

In other words, $\textrm{MEXMEX}(A)$ is the value obtained by taking the $\textrm{MEX}$ of the set of values, where each value is the $\textrm{MEX}$ of the set of elements of a contiguous subsequence of $A$.

Help ibasic find a sequence $A$ of length $N$ such that $\textrm{MEXMEX}(A)=K$.

Input

The first line contains two integers $N$ and $K$ separated by a space. $(1\le N\le 2\times 10^5;$ $0\le K\le N+1)$

Output

Output the sequence $A_1, A_2, \dots, A_N$ that satisfies the condition, separated by spaces. $(0\le A_i\le 2^{31}-1)$

If no such sequence exists, output -1 instead. If there are multiple possible sequences, output any one of them.

Examples

Input 1

6 7

Output 1

0 1 2 3 4 5