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 = map(int, input().split())
cur = 1
x = 0
a = [0] * (n + 1)
while k > 0:
    a[cur] = 1
    print(cur, end=(' '))
    if x == 0:
        cur = cur + k
        x = 1
    else:
        cur = cur - k
        x = 0
    k = k - 1
for i in range(1, n + 1):
    if a[i] == 0:
        print(i, end=' ')