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=(int(i) for i in input().split())
l=[i for i in range(1,n-k+1)]
l1=[i for i in range(n-k+1,n+1)]
k1=0
k2=k-1
for i in range(k):
    if(i%2==0):
        l.append(l1[k2])
        k2-=1
    else:
        l.append(l1[k1])
        k1+=1
print(*l)