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. 
n,k = input().split()
answer = []
answer.append(1)
appendVar = 1
lowVar = 2
highVar = 1 + int(k)

for i in range(1, int(k) + 1):
  if i % 2 == 1:
    appendVar = highVar
    highVar -= 1
    answer.append(appendVar)
  else:
    appendVar = lowVar
    lowVar += 1
    answer.append(appendVar)
for i in range(int(k)+2, int(n) + 1):
  answer.append(i)

print(*answer)

		   		  		  	 	  	  	      	