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().split())
l=[]
i=1
j=n
c=k
x=0
while(i<=j):
    if(x%2==0):
        l.append(i)
        i+=1
        x+=1
        c-=1
        if(c<=0):
            break
    elif(x%2==1):
        l.append(j)
        j-=1
        x+=1
        c-=1
        if(c<=0):
            break
if(k%2==0):
    for h in range(j,i-1,-1):
        l.append(h)
else:
    for h in range(i,j+1):
        l.append(h)
print(*l)
