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. 
import math

n,k = input().split()
n = int(n)
k = int(k)

p1 = 1
p2 = k+1
final = []
while p1<=math.ceil((k+1)/2):
    final.append(p1)
    p1 += 1
    if p2>math.ceil((k+1)/2):
        final.append(p2)
        p2 -= 1

for y in range(k+2,n+1):
    final.append(y)

for x in final:
    print(x,end = " ")
print()    
