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.PrintStream;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    private PrintStream out;
    private Scanner in;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        new Main(in, System.out).solve();
        in.close();
    }

    public Main(Scanner in, PrintStream out) {
        this.in = in;
        this.out = out;
    }

    public void solve() {
        // TODO: Solve the problem
        int n = in.nextInt();
        int k = in.nextInt();
        int[] p = new int[n];
        int x = 1;
        for(int i=0; i<n; i += 2) {
            p[i] = x++;
        }
        x = n;
        for(int i=1; i<n; i += 2) {
            p[i] = x--;
        }
//        System.out.println("k-1=" + (k-1) + ", n-1=" + (n-1));
        Arrays.sort(p, k, n);
        if( k%2 == 0 ) {
            reverse(p, k, n-1);
        }
        for(int i=0; i<n; ++i) {
            out.print(p[i] + " ");
        }
        out.println();
    }

    public void reverse(int[] a, int fromIndex, int toIndex) {
        for(int i=0; i<(toIndex-fromIndex)/2+1; ++i) {
            int left = fromIndex + i;
            int right = toIndex - i;
            int temp = a[left];
            a[left] = a[right];
            a[right] = temp;
        }
    }
}
