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.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.TreeSet;

/**
 *
 * @author таня
 */
public class KF {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
  C jk = new C();
    }
}

class C{
 PrintWriter out = new PrintWriter(System.out);
    Scanner in = new Scanner(System.in);
    int n=in.nextInt();
    int k=in.nextInt();
    int p[]= new int [n];
    C(){
        for(int i=0;i<n;i++){
        p[i]=i+1;
        }
        ans();
    for(int i=0;i<n;i++){
    out.print(p[i]+" ");
    }
    out.flush();
    }
    void ans(){
        int tek=k;
        p[0]=1;
    for(int i=1;i<=k;i++){
    if(i%2==1){
    p[i]=p[i-1]+tek;
    }
    else{
     p[i]=p[i-1]-tek;
    }
    tek--;
    }
    }
}