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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class test{
    public static void main(String... args) throws NumberFormatException, IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(st.nextToken());
        int k=Integer.parseInt(st.nextToken());
        int start=1;
        int end=k+1;
        int i=0;
        while(i<n) {
        	if(i<=k && i%2==0) {
        		System.out.print(start+" ");
        		start++;
        		i++;
        	}
        	else if(i<=k && i%2!=0) {
        		System.out.print(end+" ");
        		end--;
        		i++;
        	}
        	else {
        		System.out.print((i+1)+" ");
        		i++;
        	}
        }
    }
}
