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] = [int(x) for x in sys.stdin.readline().split()]

total = [x for x in range(1,n+1)]
final = []
diff = 0
ctr = 0
tgt = len(total)
l_val = 0
r_val = len(total) - 1
swi = True
while ctr < tgt:
    if diff < k:
        diff += 1
        if swi:
            final.append(total[l_val])
            l_val += 1
        else:
            final.append(total[r_val])
            r_val -= 1
        ctr += 1
        swi = not swi
    else:
        if swi:
            final.append(total[r_val])
            r_val -= 1
        else:
            final.append(total[l_val])
            l_val += 1
        ctr += 1
final = [str(x) for x in final]
print ' '.join(final) 
     
