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. 
var nums = readline().split(' ');
var n = parseInt(nums[0]);
var k = parseInt(nums[1]);

var st = 1;
var ed = n - 1 ;
var h = 0;
var res = n;
while(k>1)
{
	h = 1-h;
    if(h==1)
	{
	    res = res + ' ' + st;
		st++;
	}
	else
	{
	    res = res + ' ' + ed;
		ed --;
	}
	k--;
}
if(h==1)
{
    for(var i=st; i<=ed; i++)
	{
	    res = res + ' ' + i;
	}
}
else
{
    for(var i=ed; i>=st; i--)
	{
	    res = res + ' ' + i;
	}
}

print(res);