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. 
# -*- coding: utf-8 -*-
#ᕕ┌◕ᗜ◕┐ᕗ HELLO HELLO HELLO ᕕ┌◕ᗜ◕┐ᕗ

n,k = tuple(int(i) for i in raw_input().strip().split(" "))
a = []
s = 1
e = n
l = True
while k != 1:
    if l:
        a.append(s)
        s += 1
        l = False
    else:
        a.append(e)
        e -= 1
        l = True
    k -= 1
if l:
    for i in range(s,e+1):
        a.append(i)
else:
    for i in range(e,s-1,-1):
        a.append(i)
for i in range(n):
    print a[i],
