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. 
import sys
n, k = map(int, raw_input().split()) 

def print_odd_seq(n, k): 
    j = n 
    i = 1 
    for t in range((k-1)/2): 
        sys.stdout.write("%d %d " %(i, j))
        j -= 1 
        i += 1 
    for t in range(i, j+1): 
        sys.stdout.write("%d " %t)

def print_even_seq(n, k): 
    j = n 
    i = 1 
    for t in range(k/2): 
        sys.stdout.write("%d %d " %(j, i))
        j -= 1 
        i += 1 
    for t in range(i, j+1): 
        sys.stdout.write("%d " %t)


if k % 2 == 0: 
    print_even_seq(n, k)
else:
    print_odd_seq(n, k) 

sys.stdout.write("\n") 
