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:

[n, k] = list(map(int, input().split(" ")))

if k == 0:
    print(n, end=" ")
    for i in range(1, n):
        print(i, end=" ")
    print("")
elif k == n-1:
    for i in range(1, n+1):
        print(i, end=" ")
    print("")
elif k < n-1:
    beauts = 0
    numI = 2
    nums = []
    nums.append(n)
    for i in range(1, n-1):
        if beauts < k:
            nums.append(numI)
            beauts += 1
            if beauts == k:
                nums.append(1)
        else:
            nums.append(numI)
        numI += 1
    for e in nums:
        print(e, end=" ")
    print("")
else:
    print(-1)