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. 
string = input()
n, k = string.split()
n = int(n)
k = int(k)
c = n - k
perm = True
output = ""
for i in range(1, n-k + 1):
    output += str(i) + " "
i = k
output2 = ""
while i >= 1:
    if(perm):
        output2 += str(c + i) + " "
        c += i
        perm = False
    else:
        output2 += str( c - i ) + " "
        c -= i
        perm = True
    i -= 1
print(output + output2)
    	 	 			     					 		 		 		