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.*;

public class C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        boolean[] visited = new boolean[n+1];
        int idx = 2;
        visited[1] = true;
        int[] permutation = new int[n+1];
        permutation[0] = 1;
        int max = n;
        for (int i = 1; i < n; i++) {
            //System.out.println("k = " + k + ", i = " + i);
            if (k != 1) {
                permutation[i] = k + permutation[i-1];
                //System.out.println("permutation[i] = " + permutation[i]);
                visited[permutation[i]] = true;
                k--;
                permutation[i + 1] = permutation[i] - k;
                //System.out.println("k = " + k);
                //System.out.println("permutation[i+1] = " + permutation[i+1]);
                visited[permutation[i+1]] = true;
                i++;
                if (k != 1) {
                    k--;
                }
            } else {
                //System.out.println("idx = " + idx);
                while (visited[idx]) { 
                    idx++;
                    //System.out.println("idx++ --> " + idx);
                } 
                //System.out.println("permutation[i] = " + permutation[i]);
                permutation[i] = idx;
                visited[idx] = true;
            }
        }
        for (int j = 0; j < n; j++) {
            System.out.print(permutation[j] + " ");
        }
    }
}