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. 
n, k = list(map(int, input().split()))
d = []
for i in range(1, n + 1):
    d.append(i)
b = []
l, r = 0, n - 1
k -= 1
i = 0
while l <= r:
    if k != 0:
        if k % 2 == 0:
            b.append(d[l])
            l += 1
            k -= 1
        else:
            b.append(d[r])
            r -= 1
            k -= 1
    else:
        b.append(d[l])
        l += 1
    i += 1
for i in b:
    print(i, end = ' ')