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. 
lista = input()
lista = lista.split()
N = int(lista[0]);
k = int(lista[1]);

p = [1];
for indice in range (1,k+1):
    siguiente = p[indice-1] + (-1)**(indice+1)*(k-indice+1);
    p.append(siguiente)
    
for indice in range (k+1,N):
    siguiente = 1 + indice;
    p.append(siguiente)

for n in p:
    print(n)
