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.Scanner;

public class Solution {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt(); 


        int index = 0;
        int next = 1;
        int[] answer = new int[n];
        answer[index++] = next;
        boolean plus = false;

        for(int i = n-1; i > n - k; i--){
            if(index % 2 == 0){
                next = Math.abs(next - i);
                plus = false;
            }else{
                next = Math.abs(next + i);
                plus = true;
            }
            answer[index++] = next;
        }
        
        while(index < answer.length){
            answer[index] = answer[index - 1] + (plus ? -1 : 1);
            index++;
        }
        
        for(int i = 0; i < answer.length; i++){
            System.out.print(answer[i] + " ");
        }
        
    }
    
}