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. 
f = input()
n , k = map(int , f.split(' '))
x = n
y = 1
for i in range(k):
    if(i % 2 == 0):
        print(x, end=" ")
        x -= 1
    else:
        print(y, end=" ")
        y += 1
bas = 0
t = 0
if k % 2 == 0:
    bas = y
    t = 1
else:
    bas = x
    t = -1
for i in range(n - k):
    print(bas, end = " ")
    bas += t
