483_C. Diverse Permutation
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. 
```python
from collections import Counter
import string
import math
import sys
# sys.setrecursionlimit(10**6) 
from fractions import Fraction
def array_int():
    return [int(i) for i in sys.stdin.readline().split()]
def vary(arrber_of_variables):
    if arrber_of_variables==1:
        return int(sys.stdin.readline())
    if arrber_of_variables>=2:
        return map(int,sys.stdin.readline().split()) 
def makedict(var):
    return dict(Counter(var))
testcases=1
# testcases=vary(1)
for _ in range(testcases):
    n,k=vary(2)
    temp=k
    num=[i for i in range(1,n+1)]
    j=0
    for i in range(k+1):
        if i%2==0:
            print(num[j],end=" ")
            j+=1
        else:
            print(num[k],end=" ")
            k-=1
    for i in range(temp+1,n):
        print(num[i],end=" ")


        

    
```