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 $S \\gt T$.

1. 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.
2. 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.
3. 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.

Sample Input 1

3 1

Sample Output 1

2 3 1

Two permutations satisfy the condition: $(2, 3, 1)$ and $(3, 1, 2)$. For instance, the following holds for $(2, 3, 1)$:

• $\\lvert A_1 - 1\\rvert = 1 \\geq K$
• $\\lvert A_2 - 2\\rvert = 1 \\geq K$
• $\\lvert A_3 - 3\\rvert = 2 \\geq K$

Sample Input 2

8 3

Sample Output 2

4 5 6 7 8 1 2 3

Sample Input 3

8 6

Sample Output 3

-1