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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class C {
    private static Scanner scanner = new Scanner(System.in);
    
    public static void main(String[] args) {
        int n = scanner.nextInt(), k = scanner.nextInt();
        int data[] = new int[n];
        data[0] = 1;
        Set<Integer> set = new HashSet<Integer>();
        set.add(1);
        int index;
        for(index = 1; index < n && k > 0; index++) {
            if(index % 2  == 1) {
                data[index] = data[index-1] + k--;
                set.add(data[index]);
            } else {
                data[index] = data[index-1] - k--;
                set.add(data[index]);
            }
        }
        for(int i = 1; i <= n ; i++) {
            if(!set.contains(i))
                data[index++] = i;
        }
        System.out.print(data[0]);
        for(int i = 1 ; i < n ; i++)
            System.out.print(" " + data[i]);
        System.out.println();
    }
}