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. 
import math
a,b=map(int,input().split())
x1=list(range(1,math.ceil(a/2)+1))
x2=list(range(math.ceil(a/2)+1,a+1))
x2=x2[::-1]
r=[]
for i in range(b):
    if i%2==0:
        r.append(x1.pop(0))
    else:
        r.append(x2.pop(0))

x=x1+x2
x.sort()
if r[-1]>max(x):
    r+=x[::-1]
else:
    r+=x


print(' '.join(map(str,r)))
