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())

lista=[]
anterior=0
#Para conseguir esta permutación los números deben ser 1, k+1, 2, k,...,k-1, n, si n<k+2 se seguirá cumpliendo el requisito pero no terminará en n.
for j in range(1,k+2):
    if j==1:
        valor=1
    else:
        valor=(k+2-anterior) if j%2==0 else (k+3-anterior)
    lista.append(valor)
    anterior=valor
#Luego se agregan los elementos faltantes en caso de ser necesario, para todo n>k+2
for j in range(k+2, n+1):
    lista.append(j)

for n in lista:
    print(n)
