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. 



r = list(map(int, input().split()))
n = r[0]
k = r[1]
l = list()
l.append(1)
c = k
justI = 0
maxl = 0
previous = 1
print(1, end=' ')
for i in range(1,n):
    if justI == 1:
        #l.append(max(l)+1)
        print(maxl+1, end=' ')
        maxl += 1
    else:
        # l.append(l[i-1]+c)
        print(previous+c, end=' ')
        previous = previous+c
        if previous>maxl: maxl = previous
        if c>1:
            c-=1
            c*=-1
        elif c<-1:
            c+=1
            c*=-1
        else:
            justI = 1
# for i in l:
#     print(i, end=" ")




#10 4
#1 5 2 4 3 6 7 8 9 10