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. 

entrada = input()
entrada_str = list(entrada.split(" "))
entrada_int = list(map(int, entrada_str))

# entradas
tamanho = entrada_int[0]
p = entrada_int[1]
numero_anterior = 0

for i in range(1, p + 2):
    if i == 1:
        numero_atual = 1
    else:
        if i % 2 == 0:
            numero_atual = p + 2 - numero_anterior
        else:
            numero_atual = p + 3 - numero_anterior
    print(numero_atual, end=" ")
    numero_anterior = numero_atual

for i in range(p + 2, tamanho + 1):
    print(i)



  			   		   				 	     	   	 	