CF361B.Levko and Permutation

普及/提高-

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题目描述

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 $p_{i}$ 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.

输入格式

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

输出格式

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.

输入输出样例

输入#1
```
4 2
```
输出#1
```
2 4 3 1
```
输入#2
```
1 1
```
输出#2
```
-1
```

说明/提示

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.

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