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 static java.lang.System.in;

import java.io.IOException;


public class C275 {
    
    static byte[] buffer = new byte[8192];
    static int offset = 0;
    static int bufferSize = 0;
    public static void main(String args[])throws IOException
    {
        int n =readInt();
        int k =readInt();
        //int num =1;
        int val =k+1;
        int arr[] =  new int[n+1];
        System.out.print("1 ");
        arr[1]=1;
        int v =2;
        for (int i=1;i<=k;i++)
        {
            if (i%2==1)
            {
            System.out.print(val +" ");
            arr[val]=1;
            val--;
            }
            else
            {
                System.out.print(v +" ");
                arr[v]=1;
                v++;
            }
            
        }
        
        for (int i=1;i<=n;i++)
             if (arr[i]==0)
                 System.out.print(i +" ");
            
    }
    static int readInt() throws IOException{
        int number = 0;
        int s =1;
        if(offset==bufferSize){
            offset = 0;
            bufferSize = in.read(buffer);
        }
        for(;buffer[offset]<0x30 || buffer[offset]=='-'; ++offset)
        {
            if (buffer[offset]=='-')
                s=-1;
            if(offset==bufferSize-1 ){
                offset=-1;
                bufferSize = in.read(buffer);
            }
        }
        for(;offset<bufferSize && buffer[offset]>0x2f;++offset){
            number = number*0x0a+buffer[offset]-0x30;
            if(offset==bufferSize-1){
                offset = -1;
                bufferSize = in.read(buffer);
            }
        }
        ++offset;
        return number*s;
    }

}
