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. 
entrada = input()

n = int(entrada.split()[0])
k = int(entrada.split()[1])

cc =  n - k

flag = 1

i = 1
while(i <= n - k):
    print(i, end=" ")
    i += 1

i = k
while (i >= 1):
    if (flag == 1):
        if (i == 1):
            print(cc + i)
        else:
            print(cc + i, end=" ")
        cc += i
        flag = 0
    else:
        if (i == 1):
            print(cc - i)
        else:
            print(cc - i, end=" ")
        cc -= i
        flag = 1
    i -= 1
	    	  		 	   		 		 					  			