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:
from math import gcd

n,k=map(int,input().split())
ans=[0]*n
if k>n-1:
	print(-1)
	exit()
for i in range(2,k+2):
	ans[i-1]=i
rem=[1]
for i in range(k+2,n+1):
	rem.append(i)
j=0
for i in range(k+2,n+2):
	ans[i%n-1]=rem[j]
	j+=1

count=0
for i in range(n):
	if gcd(i+1,ans[i])>1:
		count+=1

if count!=k:
	print(-1)
	exit()

print(*ans)