Problem Statement

You are given positive integers $N$ and $K$. Find the lexicographically smallest permutation $A = (A_1, A_2, \ldots, A_N)$ of the integers from $1$ through $N$ that satisfies the following condition:

• $\lvert A_i - i\rvert \geq K$ for all $i$ ($1\leq i\leq N$).

If there is no such permutation, print -1.

What is lexicographical order on sequences? The following is an algorithm to determine the lexicographical order between different sequences $S$ and $T$. Below, let $S_i$ denote the $i$-th element of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$. Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same. If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ is less than $T_j$ (as a number), we determine that $S \lt T$ and quit; if $S_j$ is greater than $T_j$, we determine that $S \gt T$ and quit. If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit.

Constraints

• $2\leq N\leq 3\times 10^5$
• $1\leq K\leq N - 1$

Input

Input is given from Standard Input in the following format:

N K

Output

Print the lexicographically smallest permutation $A = (A_1, A_2, \ldots, A_N)$ of the integers from $1$ through $N$ that satisfies the condition, in the following format:

A_1 A_2 \ldots A_N

If there is no such permutation, print -1.