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 permutacaoBonita(num, numBonitos):
    permutacao = list(range(num + 1))
    numNaoBonitos = num - numBonitos
    if numNaoBonitos == 0:
        return [0, -1]
    
    if numNaoBonitos == 1:
        return permutacao

    i = 0
    if numNaoBonitos % 2 == 0:
        i = 1
    else:
        i = 2    

    while i <= numNaoBonitos:
        permutacao[i] = i + 1
        permutacao[i + 1] = i
        i += 2

    return permutacao

entrada = input().split()
num = int(entrada[0])
numBonitos = int(entrada[1])

permutacao = permutacaoBonita(num, numBonitos)
permutacao.remove(0)
print(*permutacao)