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. 
n,k = map(int,input().split())

l = [ int(i) for i in range(1,n+1)]
j=1

x=[]
i=1
inc=1
dec=n

if k ==1:
    for i in range(n):
        print(i+1,end=" ")
else:        

    while len(x)<n:

        if i%2!=0:
            x.append(inc)
            inc+=1
        else:
            x.append(dec)
            dec-=1
        i+=1    
    #print(x)

    ans=x[:k]
    #print(x)

    if ans[len(ans)-1]<ans[len(ans)-2]:
        for i in range(ans[len(ans)-1]+1,ans[len(ans)-2]):
            ans.append(i)
    else:
        for i in range(ans[len(ans)-1]-1,ans[len(ans)-2],-1):
            ans.append(i)
    for i in range(len(ans)):
        print(ans[i],end=" ")

