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.PrintWriter;
import java.util.StringTokenizer;


/**
 * TODO: Insert description here. (generated by mfahim)
 */
public class Round275_Div1_A {
  public static void main(String[] args) throws Exception {
    int n = nextInt();
    int k = nextInt();
    int st = 1, end = k;
    int[] ar = new int[n];
    for (int i = k - 1; i >= 0; i--) {
      ar[i--] = st;
      st++;
      if (i >= 0) {
        ar[i] = end;
        end--;
      }
    }
    for (int i = k; i < n; i++) {
      ar[i] = i + 1;
    }
    PrintWriter out = new PrintWriter(System.out);
    for (int i = 0; i < n; i++) {
      out.print(ar[i] + " ");
    }
    out.println();
    out.flush();
  }

  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static StringTokenizer tokenizer = new StringTokenizer("");

  static int nextInt() throws Exception {
    return Integer.parseInt(next());
  }

  static double nextDouble() throws Exception {
    return Double.parseDouble(next());
  }

  static String next() throws Exception {
    while (true) {
      if (tokenizer.hasMoreTokens()) {
        return tokenizer.nextToken();
      }
      String s = br.readLine();
      if (s == null) {
        return null;
      }
      tokenizer = new StringTokenizer(s);
    }
  }
}
