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. 
from sys import stdin,stdout,setrecursionlimit,maxint
setrecursionlimit(2*10**5)
def listInput():
 return map(long,stdin.readline().split())
def printBS(li):
 for i in xrange(len(li)-1):
  stdout.write("%d "%li[i])
 stdout.write("%d\n"%li[-1])
def sin(): return stdin.readline().rstrip()
n,k=listInput()
done=set([i for i in xrange(2,n+1)])
ans=[1]
#print done
while k:
 #print ans
 if 1<=(ans[-1]-k)<=n and (ans[-1]-k) in done:
  done.remove(ans[-1]-k)
  ans.append(ans[-1]-k)
 else: 
  done.remove(ans[-1]+k)
  ans.append(ans[-1]+k)
 k-=1
ans.extend(sorted(list(done)))
printBS(ans)