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 c6 {

    public static void main(String[] args)throws Exception {
        int n=in();
        boolean a[]=new boolean [n];
        int k=in();
        a[0]=true;
        StringBuilder b=new StringBuilder();
        boolean pr=true;
        int last=1;
        b.append(1+" ");
        for (int i=k;i>0;i--){
            if (pr){
                b.append(last+i+" ");
                last=last+i;
                a[last-1]=true;
                pr=!pr;
            }
            else{
                last=last-i;
                b.append(last+" ");
                a[last-1]=true;
                pr=!pr;
            }
        }
        for (int i=0;i<n;i++)if (!a[i])b.append(i+1+" ");
        System.out.print(b);
    }
    static BufferedReader buf=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static int in() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return Integer.parseInt(st.nextToken());
    }
    static long ll() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return Long.parseLong(st.nextToken());
    }
    static String str() throws IOException{
        if (st==null || !st.hasMoreTokens()){
            st=new StringTokenizer(buf.readLine());
        }
        return (st.nextToken());
    }
        static double dub() throws IOException{
            if (st==null || !st.hasMoreTokens()){
                st=new StringTokenizer(buf.readLine());
            }
            return Double.parseDouble(st.nextToken());
    }
}
