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

def solve():
    r = list(map(int, input().split()))
    n = r[0]
    k = r[1]
    l = list()
    l.append(1)
    c = k
    justI = 0
    maxsofar = 1
    for i in range(1,n):
        if justI == 1:
            l.append(maxsofar+1)
            maxsofar+=1
        else:
            l.append(l[i-1]+c)
            maxsofar = max(maxsofar, l[i-1]+c)
            if c>1:
                c-=1
                c*=-1
            elif c<-1:
                c+=1
                c*=-1
            else:
                justI = 1
    return l
    
def read(mode=2):
    inputs = input().strip()
    if mode == 0: return inputs  # String
    if mode == 1: return inputs.split()  # List of strings
    if mode == 2: return list(map(int, inputs.split()))  # List of integers
def write(s="\n"):
    if s is None: s = ""
    if isinstance(s, list): s = " ".join(map(str, s))
    if isinstance(s, tuple): s = " ".join(map(str, s))
    s = str(s)
    print(s, end="")
def run():
    if sys.hexversion == 50594544 : sys.stdin = open("test.txt")
    res = solve()
    write(res)
run()