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. 

def ar():
    return map(int,raw_input().split())
n,k=ar()
n1=n
j=1
di={}
t=[]
f=True
for i in range(k,0,-1):
    t.append(j)
    di[j]=True
    if f:
        j+=i
    else:
        j-=i
    f = not f
    n1-=1
for i in t:
    print i,
for j in range(1,n+1):
    if not di.get(j,False):
        print j,
##cnt1,cnt2,x,y=ar()
##if cnt1<cnt2:
##    cnt1,cnt2,x,y=cnt2,cnt1,y,x
##
##v1=cnt1
##while True:
##
##    rc1=v1/x
##    #print rc1,v1
##    if rc1+cnt1<=v1:
##        break
##    else:
##        v1+=1
##v2=v1
##while True:
##
##    rc2=v2/y
##    rc3=v2/(x*y)
##    #print rc2,rc3,cnt2,v2,"2"
##    if rc2+rc3+cnt2<=v2:
##        break
##    else:
##        v2+=1#(rc2+rc3)
##print max(v1,v2)

##from fractions import gcd
##l,r=ar()#n=int(raw_input())
##flag=0
##for i in range(l,r+1):
##    if flag:
##        break
##    for j in range(i+1,r+1):
##        if flag:
##            break
##        for k in range(j+1,r+1):
##            if flag:
##                break
##            if gcd(i,j)==1 and gcd(j,k)==1 and gcd(i,k)!=1:
##                print i,j,k
##                flag=1
##                break
##if flag==0:
##    print "-1"
