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 printList(a):
    print(" ".join(map(str, a)))

def solve():
    n, k = map(int, input().split())
    if k == 1:
        printList(range(1, n + 1))
        return

    cur = k + 1
    sh = k
    sg = -1
    ans = []
    while True:
        ans.append(cur)
        cur += sh * sg
        if not sh:
            break
        sh -= 1
        sg *= -1

    ans += list(range(k + 2, n + 1))
    printList(ans)

solve()
