Problem: 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.

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.

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.

Solution (in PYTHON3):

Solution:

def k_beautiful(n, k):
    if n <= k:
        return [-1]
    else:
        beautiful = [i for i in range(1, n+1)]
    
    # make them not beauftiful
    left = n- k - 1
    if left % 2 == 0:
        for i in range(k+1, n, 2):
            beautiful[i], beautiful[i+1] = beautiful[i+1], beautiful[i] 
    else:
        for i in range(k+1, n-1, 2):
            beautiful[i], beautiful[i+1] = beautiful[i+1], beautiful[i]
        beautiful[0], beautiful[-1] = beautiful[-1], beautiful[0]
        
        
    return beautiful

def print_l(l):
    string = ""
    for item in l:
        string += str(item) + " "
    if len(string) > 1:
        string = string[0:len(string) - 1]
    print(string)
    
        
def main():
    i = input().split()
    n = int(i[0])
    k = int(i[1])
    print_l(k_beautiful(n, k))

main()