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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
  public static void main(String[] args) {
    MyScanner sc = new MyScanner();
    int n = sc.nextInt();
    int k = sc.nextInt();
    if (k % 2 == 0) {
      for (int i = 1; i <= k / 2; ++i) {
        System.out.print(i + " " + (k + 2 - i) + " ");
      }
      System.out.print(((k + 2) / 2)+ " ");
    } else {
      for (int i = 1; i <= (k + 1) / 2; ++i) {
        System.out.print(i + " " + (k + 2 - i) + " ");
      }
    }
    for (int i = k + 2; i <= n; ++i) {
      System.out.print(i + " ");
    }
  }

  public static class MyScanner {
    BufferedReader br;
    StringTokenizer st;
    
    public MyScanner() {
      br = new BufferedReader(new InputStreamReader(System.in));
    }
    
    int nextInt() {
      return Integer.parseInt(next());
    }
    
    long nextLong() {
      return Long.parseLong(next());
    }
    
    double nextDouble() {
      return Double.parseDouble(next());
    }
    
    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        }
        catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }
    
    String nextLine() {
      String str = "";
      try { str = br.readLine(); }
      catch (IOException e) { e.printStackTrace(); }
      return str;
    }
  }
}
