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;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class C {
    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;
    
    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }

        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    
    public void solve() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);

        int n = nextInt();
        int k = nextInt();
        boolean [] printed = new boolean[n+1];
        int lower = 1;
        int upper = 1 + k;
        
        while(lower != upper) {
            out.print(lower+" ");
            printed[lower] = true;
            lower++;

            if(lower != upper) {
                out.print(upper+" ");
                printed[upper]  = true;
                upper--;
            }
        }
        int i = 1;
        while(i <= n) {
            if(!printed[i])
                out.print(i+" ");
            i++;
        }        
        out.close();
    }
    
    public static void main (String [] args) throws IOException {
        new C().solve();
    }
}
