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


public class C {
    private void processInput() throws IOException {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();

        go(n, k);

        in.close();
    }

    private void go(int n, int k) {

        int curr = 1;
        int mult = 1;
        int max = 1;
        System.out.printf(Locale.ENGLISH, "%d", curr);
        int K = k;
        for (int i = 1; i < n; i++) {
            
            if (k > 0) {
                curr = curr + (mult * k);
                k--;
                mult *= -1;
            } else {
                curr = max + 1;
            }
            max = Math.max(max, curr);
            System.out.printf(Locale.ENGLISH, " %d", curr);
        }
        
    }

    public long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static void main(String[] args) throws Exception {
        C main = new C();
        main.processInput();
    }
}
