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. 
__author__ = 'xywang'
import sys

class CodeForces:
    def getResult(self):
        n, m = map(int, sys.stdin.readline().split(" "))
        previous = 0
        after = previous
        while after <= m/2:
            previous += 1
            if previous == m - after + 1:
                print previous,
                break
            print previous,
            print m - after + 1,
            after = previous
        for i in range(m + 2, n + 1):
            print i,





def main():
    code = CodeForces()
    code.getResult()

if __name__ == "__main__":
    main()