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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.Locale;



public class B {

    
    public static void main(String[] args) {
        Locale.setDefault(Locale.US);
        InputStream inputstream=System.in;
        OutputStream outputstream=System.out;
        FastReader in=new FastReader(inputstream);
        PrintWriter out=new PrintWriter(outputstream);
        TaskA solver=new TaskA();
        solver.solve(1,in,out); 
        out.close();


    }

}

class TaskA
{
    public void solve(int testnumber,FastReader in,PrintWriter out)
    {
    int n=in.ni();
    int k=in.ni();
    int i=1;
    int arr[]=new int[n];
    arr[0]=1;
    arr[1]=k+1;
    k--;
    boolean flag=false;
    for(i=2;i<n;i++)
    {
        
        if(i%2!=0 && k!=0)
        {
            arr[i]=arr[i-2]-1;
            k--;
        }
        else if(i%2==0 && k!=0)
        {
        arr[i]=arr[i-2]+1;
        k--;
        }
        else
        {
            flag=true;
            break;
        }
        
    }
    if(flag)
    for(int j=n-1;j>=i;j--)
        {
        arr[j]=n;
        n--;
        }
    for(int m: arr)
        out.print(m+" ");
    
}
}
class FastReader {
    public InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(InputStream stream)
    {
        this.stream = stream;
    }
 
    public FastReader()
    {
 
    }
 
    public int read()
    {
        if (numChars == -1)
        {
            throw new InputMismatchException ();
        }
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read (buf);
            } catch (IOException e)
            {
                throw new InputMismatchException ();
            }
            if (numChars <= 0)
            {
                return -1;
            }
        }
        return buf[curChar++];
    }
 
    public int ni()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }
 
    public String ns()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        StringBuilder res = new StringBuilder ();
        do
        {
            res.appendCodePoint (c);
            c = read ();
        } while (!isSpaceChar (c));
        return res.toString ();
    }
 
    public boolean isSpaceChar(int c)
    {
        if (filter != null)
        {
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }
 
    public static boolean isWhitespace(int c)
    {
        return c==' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public int[] iArr(int n)
    {
        int a[] = new int[n];
        for (int i = 0; i < n; i++)
        {
            a[i] = ni ();
        }
        return a;
    }
 
    public String next()
    {
        return ns ();
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }


}
