Levko and Permutation

1000ms

262144K

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 p_i of permutation p₁, p₂, ... , 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 ≤ 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.

Sample Input:

4 2

Sample Output:

2 4 3 1

Sample Input:

1 1

Sample 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.

Informação

Provedor Codeforces

Código CF361B