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. 
def main():
    n,k=map(int,raw_input().strip().split())    

    med=(n+1)/2

    sol=[0]*(k+1)

    sol[0]=(k+2)/2
    mult=1
    for i in range(1,k+1):
        sol[i]=sol[i-1]+mult*i
        mult*=-1
    
    for i in range(k+1):sol[i]+=(n-k-1)

    sol=[i+1 for i in range(n-k-1)]+sol
    print " ".join(map(str,sol))
    







main()