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 = map(int, input().strip().split(' '))
if n==1:
    print(1)
elif n==2:
    print('1 2')
else:
    if k==1:
        for i in range(1,n+1):
            print(i,end=" ")
        print()
    elif k==n-1:
        i1=1
        i2=n
        for i in range(1,n+1):
            if i%2!=0:
                print(i1,end=" ")
                i1+=1
            else:
                print(i2,end=" ")
                i2-=1
    else:
        for i in range(1,n-k):
            print(i,end=" ")
        i1=i+1
        i2=n
        for j in range(1,k+2):
            if j%2!=0:
                print(i1,end=" ")
                i1+=1
            else:
                print(i2,end=" ")
                i2-=1