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,math
n,k = map(int,input().split(' '))
arr = [None]*n
even = 1
odd = n
for i in range(n):
    if i%2==0:
        arr[i]=even
        even+=1
    else:
        arr[i]=odd
        odd-=1
minn = min(arr[k-1:])
if arr[k-1]>minn:
    num = arr[k-1]
    for i in range(k-1,n):
        arr[i] = num
        num-=1
else:
    num = arr[k-1]
    for i in range(k-1,n):
        arr[i] = num
        num+=1
arr = map(str,arr)
print(' '.join(arr))
