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. 
#l1 = int(input())
l2 = input().split()

x = int(l2[0])
y = int(l2[1])
c = x - y

d = True;

for i in range (1, x - y + 1):
    print(str(i) + " ", end = '')

v = y
while (v >= 1):
  if (d):
      print(str(c+v) + " ", end = '')
      c += v;
      d = False;

  else:
      print(str(c-v) + " ", end = '')
      c -= v;
      d = True;

  v -= 1



 		 		 			 	      	  	  	  			