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
from sys import stdin, stdout
from collections import deque
from copy import deepcopy
from bisect import bisect_right
from heapq import heapify,heappop,heappush,heapreplace
rem = 10 ** 9 + 7
sys.setrecursionlimit(10 ** 6)
take = lambda: map(int, stdin.readline().split())

n,k=take()
if k==1:
    print ' '.join(map(str,range(1,n+1)))
    exit()
arr=[]
left=1
right=n
diff=-1
while(left<=right):
    arr.append(left)
    left+=1
    diff+=1
    if diff==k-1:
        for i in range(left,right+1):
            arr.append(i)
        break
    if left>right:
        break
    diff+=1
    arr.append(right)
    right-=1
    if diff==k-1:
        for i in range(right,left-1,-1):
            arr.append(i)
        break
print ' '.join(map(str,arr))









