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 sys
n, k = map(int, input().split())
left = 1
right = n
turn = 0
while k > 0:
    if turn == 0:
        sys.stdout.write(str(left))
        left += 1
    else:
        sys.stdout.write(str(right))
        right -= 1
    sys.stdout.write(" ")
    k -= 1
    turn = 1 - turn
if turn == 1:
    cur = left
    while cur <= right:
        sys.stdout.write(str(cur))
        sys.stdout.write(" ")
        cur += 1
else:
    cur = right
    while cur >= left:
        sys.stdout.write(str(cur))
        sys.stdout.write(" ")
        cur -= 1