Score : $600$ points

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.

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.

3 1

2 3 1

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

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

8 3

4 5 6 7 8 1 2 3

8 6

-1