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())
if k == 1:
    for i in range(1, n+1):
        print(i, end=' ')
    sys.exit();
for i in range(0, k//2):
    print(i+1, n-i, end=' ')
if k%2:
    z = k//2+3
    for i in range(n-k//2, k//2+2, -1):
        z = i
        print(i, end=' ')
    print(z-2, z-1)
else:
    for i in range(n-k//2, k//2, -1):
        print(i, end=' ')

