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

sequence = []
digitos = []
prox_asc = 1
prox_desc = k+1
turno = False

for _ in range(k+1):
	digitos.append(abs(prox_asc- prox_desc))

	if turno:
		sequence.append(prox_desc)	
		prox_desc-=1
	else:
		sequence.append(prox_asc)	

		prox_asc+=1
	turno = not turno


for i in range(k+2,n+1):
    sequence.append(i)

# if len(sequence) < n+1:
# 	for i in range(k+2, n+1):
# 		if i not in sequence:
# 			sequence.append(i)

print(' '.join([str(x) for x in sequence]))
# print(digitos)
