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 CF4 {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int k = input.nextInt();
        int[] table = new int[n];
        int co = 1;
        int min = 0;
        for (int i = 1; i <= k; i++) {
           table[i] = (i + 1) / 2 * co;
           min = Math.min(table[i], min);
           co *= -1;
        }
        for (int i = k + 1; i < n; i++) {
            table[i] = table[i - 1] - co;
            min = Math.min(table[i], min);
        }
        for (int i = 0; i < n; i++) {
            table[i] -= min - 1;
        }
        for (int i = 0; i < n; i++) {
            if ((i != 0) & (i != (n-1))) {
                System.out.print(" ");
                System.out.print(table[i]);
            } else if (i == 0) {
                System.out.print(table[i]);
            } else {
                System.out.print(" ");
                System.out.println(table[i]);
            }
        }
        
    }
    
}
