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Description

Given two positive integers $N$ and $K$, find the lexicographically smallest permutation of the integers $1, \ldots, N$ which satisfies the following condition:

Note: A sequence $v_1, ..., v_N$ is lexicographically smaller than another sequence $v'_1, ..., v'_N$ if there exists $1 \leq i \leq N$ such that $v_j = v'_j$ for all $1 \leq j < i$, and $v_i < v'_i$. For example, $(1,2,3)$ is lexicographically smaller than $(2, 1, 3)$, which is lexicographically smaller than $(2,3,1)$.

Format

Input

Two numbers $N$, $K$

Output

Print the lexicographically smallest permutation of the integers $1, \ldots, N$ which satisfies the above condition, in the format $A_1 \, A_2 \, \dots \, A_N$.

If there is no such permutation, print $-1$.

Samples

3 1

2 3 1

Two permutations satisfy the condition, (2,3,1) and (3,1,2). For instance, for (2, 3, 1) we have:

$|A_1 - 1| = 1 \geq K$

$|A_2 - 2| = 1 \geq K$

$|A_3 - 3| = 2 \geq K$

8 3

4 5 6 7 8 1 2 3

8 6

-1

Limitation

$2\leq N\leq 3\times 10^5$

$1\leq K\leq N-1$