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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.HashSet;
import java.util.Map;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class solver {
    
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;
    
    static final boolean OJ = System.getProperty("ONLINE_JUDGE") != null;
    
    void init() throws FileNotFoundException{
        if (OJ){
          in = new BufferedReader(new InputStreamReader(System.in));
          out = new PrintWriter(System.out);
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }
    
    String readString() throws IOException{
        while (tok == null || !tok.hasMoreTokens()){
            tok = new StringTokenizer(in.readLine()," :");
        }
        return tok.nextToken();
    }
    
    int readInt() throws NumberFormatException, IOException{
        return Integer.parseInt(readString());
    }
    
    double readDouble() throws NumberFormatException, IOException{
        return Double.parseDouble(readString());
    }
    
    long readLong() throws NumberFormatException, IOException{
        return Long.parseLong(readString());
    }
    long time;
    void run(){
        try{
            time = System.currentTimeMillis();
            init();
            solve();
            if (!OJ) System.err.println(System.currentTimeMillis() - time);
            out.close();
            in.close();
        }catch (Exception e){
            e.printStackTrace();
        }
    }
    
    long gcd(long a, long b){
        if (a == 0) return b;
        return gcd(b % a, a);
    }
       
    void solve() throws NumberFormatException, IOException{
        int n = readInt();
        int k = readInt();
        
        int first = 1;
        int last = n;
        int c = 0;
        for (int i=0;i<k;i++){
            if (c == 0){
                out.print(first+" ");
                first++;
            }else{
                out.print(last+" ");
                last--;
            }
            c = 1 - c;
        }
        if (c == 0){
            for (int i=last;i>=first;i--){
                out.print(i+" ");
            }
        }else{
            for (int i=first;i<=last;i++){
                out.print(i+" ");
            }           
        }
        
        
    }

    public static void main(String[] args) {
        new solver().run();
    }

}