#P361B. Levko and Permutation
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ID: 2821
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Levko and Permutation
No submission language available for this problem.
Description
Levko 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 pi of permutation p1, p2, ... , pn is good if gcd(i, pi) > 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.
The single line contains two integers n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ n).
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.
Input
The single line contains two integers n and k (1 ≤ n ≤ 105, 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.
Samples
4 2
2 4 3 1
1 1
-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.