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 itertools
import math

def main():
	n, k = map(int, input().split())
	a = 1
	b = n
	res = []
	for i in range(k - 1):
		if i % 2:
			res.append(a)
			a += 1
		else:
			res.append(b)
			b -= 1
	if k % 2:
		res += range(b, a - 1, -1)
	else:
		res += range(a, b + 1)
			
	print(" ".join(map(str, res)))

if __name__ == "__main__":
	main()
