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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class A_Div2_275 {
    public static void main(String[]arg) throws IOException
    {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n,k,i,val,c;
        String ans = "";
        n = Integer.parseInt(st.nextToken());
        k = Integer.parseInt(st.nextToken());
        val = 1;c = 0;
        System.out.print(1);
        int f = -1;
        for(i = k; i >= 1; i--,c++)
        {
            val += i*(f*-1);
            f *= -1; 
            System.out.print(" " + val);
        }
        //System.out.println(ans+".."+c);
        val = 1 + k;
        for(i = c+1; i < n; i++)
        {           
            val += 1;
            System.out.print(" " +val);
        }
        System.out.println();
    }
}   
