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.util.StringTokenizer;

public class CR275_diverse_permutation {

    public static void main(String... args) throws IOException {
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        int k = sc.nextInt();

        StringBuilder sb = new StringBuilder();
        for (int i = 1; i <= n - k; i++) {
            sb.append(i).append(' ');
        }

        int up = n;
        int down = n - k + 1;
        while (up > down) {
            sb.append(up--).append(' ').append(down++).append(' ');
        }
        if (up == down){
            sb.append(up);
        }

        System.out.println(sb.toString());
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        private long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}
