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. 
#!/usr/bin/python2
# -*- coding: utf-8 -*-

import sys
import os

def main():
    n, k = map(int, sys.stdin.readline().split())
    a = 2
    b = n
    c = 1
    print 1,
    while k > 1:
        if c:
            print b,
            b -= 1
        else:
            print a,
            a += 1
        c ^= 1
        k -= 1
    if c:
        while a <= b:
            print a,
            a += 1
    else:
        while a <= b:
            print b,
            b -= 1
    print


if __name__ == '__main__':
    main()
