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. 
params = list(map(int,list(input().split())))
n = params[0]
k = params[1]

def do_shit():
    lst = [1,k+1]
    count = 2
    
    while len(lst) <= n:
        lst.append(count)
        if abs(lst[-1] - lst[-2]) == 1:
            break
        lst.append(k - count + 2)
        if abs(lst[-1] - lst[-2]) == 1:
            break
        count += 1
    
    for r in range(len(lst)+1, n+1):
        lst.append(r)
    
    return lst

if k == 1:
    string = ''
    for r in range(1,n+1):
        string += str(r)
        string += ' '
    print(string[:-1])
else:
    lst = do_shit()
    string = ''
    for i in lst:
        string += str(i)
        string += ' '
    print(string[:-1])    
		   	 	 	 			 	 		  			     		