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.*;
public class DiversePermutation {

    public static void main(String[] args){
        Scanner k = new Scanner(System.in);
//      System.nanoTime();
        int total = k.nextInt();
        int diff = k.nextInt();
//      int [] perm = new int[total];
        int a = 0;
        int b = total-1;
        int d = 0;
//      int i = 1;
        boolean [] used = new boolean[total];
        Arrays.fill(used, false);
        for(int p=0;p<total;p++)used[p]=false;
//      String used = "";
        //      if(total - diff >1){
//      System.out.print("1 ");
//      i++;
        for(int i=0;i<diff;i++){
            used[(i&1) == 0 ? a : b]=true; 
            if((i&1) == 0){
//              perm[i]=a;
                System.out.print(1 + (a++));
            }else{
//              perm[i]=b;
                System.out.print(1 + (b--));
            }
            System.out.print(" ");
//          if(i>=1 && diff-d > 0)d++;
//          i++;
        }
//          System.out.println(Arrays.toString(used));
        
        if((diff&1) == 1){
            for(int i=0;i<total;i++){
                if(used[i] == false)System.out.print((i+1) + " ");
            }
        }else{
            for(int i = total-1; i>=0;i--){
                if(used[i] == false)System.out.print((i+1) + " ");
            }

    }
    //      for(int j=0;j<perm.length;j++){
    //          System.out.print(perm[j] + " ");
//  System.out.print("\n"+System.nanoTime());
}
}
