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. 
import sys
import math
  
n, k = [int(x) for x in (sys.stdin.readline()).split()]
res = []

z = 1
for i in range(n, 1, -1):
    if(i > k):
        res.append(str(i))
    else:
        z = i
        break
l = z 
j = 1   
for i in range(1, z + 1):
    if(i % 2 != 0):
        res.append(str(j))
        j += 1
    else:
        res.append(str(z))
        z -= 1
    
print(" ".join(res[::-1]))