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. 
int_inp   = lambda: int(input()) #integer input
strng     = lambda: input().strip() #string input
strl      = lambda: list(input().strip())#list of strings as input
mul       = lambda: map(int,input().split())#multiple integers as inpnut
mulf      = lambda: map(float,input().split())#multiple floats as ipnut
seq       = lambda: list(map(int,input().split()))#list of integers
import math
from collections import Counter,defaultdict

k,m = mul()
a = [0]*k
q =1
print(1,end=" ")
i = 1
for i in range(1,m+1):
    q+=m
    print(q,end=" ")
    if m>0:
        m = -(m-1)
    else:
        m = -(m+1)
    i+=1
while i<k:
    print(i+1,end=' ')
    i+=1
