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 inp = readline().split(" ").map(function(x){return parseInt(x);});
var n = inp[0];
var k = inp[1];

var sign = true;
var res = [];
for(var i=0; i < n-k; i++){
	res.push(i+1);
}
for(var i=0; i < k; i++){
	if (sign){
		res.push(res[n-k+i-1] + (k-i));
	} else {
		res.push(res[n-k+i-1] - (k-i));
	}
	sign = !sign;
}
var resS = "";
for(var i=0; i < n; i++)
	resS += res[i] + " ";
print(resS);