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 C {

    public static void main(String[] args) {
        try {
            InputScanner scanner = new InputScanner();
            int n = scanner.nextInt();
            int k = scanner.nextInt();
            int start = n - k;
            int startK = k;
            int start2 = start - 1;
            while (k > 0) {
                int tmp = n - k;
                System.out.print(n + " " + tmp + " ");
                n--;
                k -= 2;
            }
            if (startK % 2 == 0) System.out.print(n + " ");
            while (start2 > 0) {
                System.out.print(start2 + " ");
                start2--;
            }
        } catch (IOException e) {
        }
    }

    static class InputScanner {

        BufferedReader br;
        StringTokenizer st;

        public InputScanner() {
            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();
            next.length();
            return Integer.parseInt(next);
        }
    }
}