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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分