Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
maxn = 100000+10
ans = [0 for i in range(maxn)]
vis = [0 for i in range(maxn)]

s = input()
arr = s.split()
n = int(arr[0])
k = int(arr[1])

ans[0] = 1
cnt = k
for i in range(1, k+1):
    tmp = ans[i-1] + cnt
    if tmp > k+1 or vis[tmp]==1:
        tmp = ans[i-1]-cnt
    vis[tmp] = 1
    ans[i] = tmp
    cnt -= 1
print(1, end='')
for i in range(1,k+1):
    print('', ans[i], end='')
for i in range(k+1, n):
    print('', i+1, end='')
print()

 	    		 	  				  		  		   	 	