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. 
s = input().split()
n = int(s[0])  # ���-�� ����� � ������������
k = int(s[1])  # ���-�� ��������� ���������
max = k+1
l = 1
print(l, end = ' ')

for i in range(k):  # ���������� ����� � ����������������� ����������
    if i % 2 == 0:
        l += k
    else:
        l -= k
    k -= 1
    print(l, end = ' ')
    
if max < n:  # ���������� ����� � ����������� ����������
    for i in range(max+1, n+1):
        print(i, end = ' ')