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 -*-
import sys
def some_func():
    """
    """

    n,s = map(int, sys.stdin.readline().split())

    strat = 1
    end = n
    count = 1
    while True:
        if s:
            if count%2:
                print strat,
                strat+=1
            else:
                print end,
                end -=1
            s-=1
            count+=1
        else:
            if count%2:
                for i in range(end,strat-1,-1):
                    print i,
            else:
                for i in range(strat,end+1):
                    print i,
            break


if __name__ == '__main__':
    some_func()



