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. 
'''f=open('input.txt')
g=open('output.txt', 'w')
nooftest=int(f.readline().strip())'''
#import cmath
import math
import time
n,k=map(int,raw_input().split())
diff=k
print 1,
a=1
m=0
while diff!=0:
    print a+(diff*(pow(-1,m))),
    a=a+(diff*(pow(-1,m)))
    diff-=1
    m+=1
i=k+2
while i<n+1:
    print i,
    i+=1
