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.util.*;
import java.math.*;
import java.io.*;
public class CF483C {
    public static void main(String args[]) {
        InputReader in=new InputReader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int n=in.nextInt();
        int k=in.nextInt();
        int l=1,r=n;
        for(int i=0;i<k-1;i++) {
            if(i%2==0) {
                out.print(l+" ");
                l++;
            }else {
                out.print(r+" ");
                r--;
            }
        }
        if(k%2==0) {
            for(int i=r;i>=l;i--) out.print(i+" ");
        }else {
            for(int i=l;i<=r;i++) out.print(i+" ");
        }
        out.println("");
        out.close();
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader=new BufferedReader(new InputStreamReader(stream));
        tokenizer=null;
    }

    public String next() {
        while(tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            }catch(IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
}