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. 
def getLine():
    return list(map(int,input().split()))


n,k = getLine()

l = [0]*n
for i in range(n):
    if i%2 == 0:l[i] = i//2+1
    else : l[i] = n - l[i-1]+1


ans=l
for i in range(k,n):
    if k%2 == 0:l[i] = l[i-1]-1
    else : l[i] = l[i-1]+1

for i in ans:
    print(i,end=" ")