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.IOException;
import java.util.Scanner;


public class Main {

    
    
    public static void main(String[] args) throws NumberFormatException, IOException
    {
        
        Scanner sc = new Scanner(System.in);
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt(), k = sc.nextInt();
        int[] arr = new int[n];
        for(int cur = 1, nxt = n, d = 1, idx = 0; idx < n; idx++)
        {
            if(k == 1)
            {
                arr[idx] = cur;
                cur += d;
            }
            else
            {
                arr[idx] = cur;
                if(k != 1)
                {
                    int tmp = cur;
                    cur = nxt;
                    nxt = tmp + d;
                    d *= -1;
                    k--;
                }
            }
                
        }
        for(int i = 0; i < n - 1; i++)
            sb.append(arr[i]+" ");
        sb.append(arr[n-1]);
        System.out.println(sb);
    }


}
