Codeforces Round 210 (Div. 2) |
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Finished |

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constructive algorithms

math

number theory

*1200

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B. Levko and Permutation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLevko loves permutations very much. A permutation of length *n* is a sequence of distinct positive integers, each is at most *n*.

Let’s assume that value *gcd*(*a*, *b*) shows the greatest common divisor of numbers *a* and *b*. Levko assumes that element *p*_{i} of permutation *p*_{1}, *p*_{2}, ... , *p*_{n} is good if *gcd*(*i*, *p*_{i}) > 1. Levko considers a permutation beautiful, if it has exactly *k* good elements. Unfortunately, he doesn’t know any beautiful permutation. Your task is to help him to find at least one of them.

Input

The single line contains two integers *n* and *k* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *k* ≤ *n*).

Output

In a single line print either any beautiful permutation or -1, if such permutation doesn’t exist.

If there are multiple suitable permutations, you are allowed to print any of them.

Examples

Input

4 2

Output

2 4 3 1

Input

1 1

Output

-1

Note

In the first sample elements 4 and 3 are good because *gcd*(2, 4) = 2 > 1 and *gcd*(3, 3) = 3 > 1. Elements 2 and 1 are not good because *gcd*(1, 2) = 1 and *gcd*(4, 1) = 1. As there are exactly 2 good elements, the permutation is beautiful.

The second sample has no beautiful permutations.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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