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,input().split())
    first = 1
    last = n
    ans = []

    k -= 1
    if k == 0:
        while first <= last:
            ans.append(first)
            first += 1
        for i in ans:
            print(i,end = ' ')
        return
    ans = [1]
    first += 1
    count = 0
    while count != k:
        if count%2 == 0:
            ans.append(last)
            last -= 1
        else:
            ans.append(first)
            first += 1
        count += 1
    if ans[-1] <= n//2:
        while len(ans) != n:
            ans.append(ans[-1]+1)
    else:
        while len(ans) != n:
            ans.append(ans[-1]-1)

    for i in ans:
        print(i,end = ' ')

main()
