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;

/**
 *
 * @author giovanny
 */
public class DiversePermutation {

    DiversePermutation(int n, int k) {
        int kpos;
        int kval = n;
        int j = 0;
        if (k % 2 == 0) {//multiplo de 2
            for (int i = 0; i < n; i++) {
                if (i % 2 == 0 && k > 1) {
                    System.out.print(kval + " ");
                    k -= 2;
                    kval--;
                } else {
                    System.out.print((j + 1) + " ");
                    j++;
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                if (i % 2 == 1 && k > 1) {
                    System.out.print(kval + " ");
                    k-=2;
                    kval--;
                } else {
                    System.out.print((j + 1) + " ");
                    j++;
                }
            }

        }
        System.out.println("");
    }

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] linea = (in.readLine()).split(" ");
        int n, k;
        n = Integer.parseInt(linea[0]);
        k = Integer.parseInt(linea[1]);

        DiversePermutation DP = new DiversePermutation(n, k);
    }
}
