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. 
a=input()
a=a.split()
b=[0]*int(a[0])
f=[]
mensaje=" "
mensaje1=""
z=0
nana=0


if int(a[1])==1:
        for p in range (int(a[0])):
                b[p]=str(p+1)
        mensaje1=' '.join(b)
else:
        n1=1
        nm=int(a[1])+1
        ku=0
        while ku<(int(a[1])+1):
                if ku%2==0:
                        f.append(str(nm))
                        nm=nm-1
                else:
                        f.append(str(n1))
                        n1=n1+1
                ku=ku+1
        for k in range (int(a[1])+2,int(a[0])+1):
                f.append(str(k))
        mensaje1=' '.join(f)
print(mensaje1)