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 = [int(i) for i in input().split()]
if k == 2:
    print(1, 3, 2, end=" ")
    for i in range(4, n + 1):
        print(i, end=" ")
elif k % 2 == 0:
    low = 1
    high = n
    for i in range(k - 1):
        if i % 2 == 1:
            print(low, end=" ")
            low += 1
        else:
            print(high, end=" ")
            high -= 1
    for i in range(low, high + 1):
        print(i, end=" ")
else:
    low = 1
    high = n
    for i in range(k - 1):
        if i % 2 == 0:
            print(low, end=" ")
            low += 1
        else:
            print(high, end=" ")
            high -= 1
    for i in range(low, high + 1):
        print(i, end=" ")
print()