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())
L = []
for i in range(n + 1):
    L.append(i)
k1 = k
s = (n * (n + 1)) / 2 - 1
L[1] = 0
L[k + 1] = 0
print('1', k + 1, end = ' ')
k = k - 1
b = k + 2
while s > 0:
    if k == 0:
        break
    if b - k > 0 and L[b - k] != 0:
        print(L[b - k], end = ' ')
        L[b - k] = 0
        s -= b - k
        b = abs(b - k)
        k -= 1
    else:
        print(L[b + k], end = ' ')
        L[b + k] = 0
        s -= b + k
        b = abs(b + k)
        k -= 1
for i in range(len(L)):
    if L[i] != 0:
        print(L[i], end = ' ')

            
