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())
t = []
t.append(1)
h=1
p=0
for i in range(k,0,-1):
    
    if(p%2==0):
        o = t[h-1]+i
        p+=1
        t.append(o)
        h+=1
    else:
        t.append(t[h-1]-i)
        h+=1
        p+=1
for i in range(k+2,n+1):
    t.append(i)
for i in t:
    print(i,end=" ")
    