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.*;
import java.math.BigInteger;
import java.util.*;


public class A {

    void solve() throws IOException {
        int n=nextInt();
        int k=nextInt();
        int i=2;
        int j=n;
        boolean q=false;
        out.print("1 ");
        for(int w=0;w<k-1;w++){
            if(q)out.print((i++)+" ");
            else out.print((j--)+" ");
            q=!q;
        }
        while(i<=j){
            if(!q)out.print((i++)+" ");
            else out.print((j--)+" ");
        }
    }

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

    void run() throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
//      reader = new BufferedReader(new FileReader("input.txt"));
        tokenizer = null;
        out = new PrintWriter(new OutputStreamWriter(System.out));
//      out = new PrintWriter(new FileWriter("output.txt"));
        solve();
        reader.close();
        out.flush();

    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter out;

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}
