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. 
from sys import stdin, stdout
import math, collections
mod = 998244353
def swap(arr, i, j):
    arr[i], arr[j] = arr[j], arr[i]
#for _ in range(int(stdin.readline())):
n, k = map(int, stdin.readline().split())
arr = [1]
s = set()
i = 1
while len(s)<k-1:
    if len(arr)%2==1:
        arr.append(n-i//2)
    else:
        arr.append(i//2+1)
    s.add(abs(arr[-2]-arr[-1]))
    i+=1
if len(arr)%2==0:
    while len(arr)<n:
        arr.append(arr[-1]-1)
else:
    while len(arr)<n:
        arr.append(arr[-1]+1)
print(*arr)