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 dust i have come dust i will be

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

i=1
a=[]
for j in range(n//2):
    a.append(i)
    a.append(n-i+1)
    i+=1

if n%2==1:
    a.append(n//2+1)

for i in range(k):
    print(a[i],end=' ')

if k<n and a[k-1]>a[k]:
    s=a[k-1]-1
    for i in range(k,n):
        print(s,end=' ')
        s-=1

else:
    s=a[k-1]+1
    for i in range(k,n):
        print(s,end=' ')
        s+=1
