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/python3

import sys

if __name__ == '__main__':
    
    n, k = map(int, sys.stdin.readline().split())
    l = []
    i = 1
    j = k + 1
    while i <= j:
        l.append(str(i))
        i += 1
        if j > i:
            l.append(str(j))
            j -= 1
    for i in range(k+2, n+1):
        l.append(str(i))
    
    print(' '.join(l))

