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.PrintStream;
import java.util.ArrayList;
import java.util.Scanner;

/**
 * Created by Oleg on 19.11.2014.
 */
public class C {
    public static Scanner cin = new Scanner(System.in);
    public static PrintStream cout = System.out;

    public static void main(String[] args) {
        int n = cin.nextInt(), k = cin.nextInt();
        ArrayList<Integer> answer = new ArrayList<Integer>();
        int max = n, min = 1;
        boolean lastmin = true;
        while(answer.size() < n){
            if(k == 1){
                if(lastmin) {
                    answer.add(min);
                    min++;
                }else {
                    answer.add(max);
                    max--;
                }
            }else{
                if(answer.size() == 0){

                    answer.add(max);
                    max--;

                }else{
                    if(answer.size() % 2 == 1){
                        answer.add(min);
                        min++;
                        k--;
                        lastmin = true;
                    }else{
                        answer.add(max);
                        max--;
                        k--;
                        lastmin = false;
                    }
                }
            }
        }
        for(int i = 0; i < answer.size(); i++){
            System.out.print(answer.get(i) + " ");
        }
        System.out.println();
    }
}
