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. 
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import java.util.*;
public class Main
{
    void sort(int arr[])
    {
        int n = arr.length;
        int count = 0;
        String str = "";
 
        for (int i = 0; i < n-1; i++)
        {
            int min_idx = i;
            for (int j = i+1; j < n; j++)
                if (arr[j] < arr[min_idx])
                    {
                        //System.out.println(i+" "+j);
                        min_idx = j;
                        //count++;
                        
                    }
            if(min_idx != i)
            {
                count++;
                int temp = arr[min_idx];
                arr[min_idx] = arr[i];
                arr[i] = temp;
                str += String.valueOf(i) + " "+ String.valueOf(min_idx) + "\n";
            }
        }
        System.out.println(count+"\n"+str);
    }
	public static void main(String[] args) {
		//System.out.println("Hello World");
		Scanner sc = new Scanner(System.in);
		
		Main ob = new Main();
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		int min = 1;
		int max = k+1;
		
        //int arr[] = new int[n+1];
        
        for(int i = 1;i<=k+1;i++)
        {
            if(i%2 == 1)
            {
                //arr[i] = min;
                
                System.out.print(min+" ");
                min++;
            }
            else{
                
                System.out.print(max+" ");
                max--;
            }
        }
        for(int i = k+2;i<=n;i++)
        {
            System.out.print(i+" ");
        }
        
	}
}
