Problem: After a team finished their training session on Euro football championship, Valeric was commissioned to gather the balls and sort them into baskets. Overall the stadium has n balls and m baskets. The baskets are positioned in a row from left to right and they are numbered with numbers from 1 to m, correspondingly. The balls are numbered with numbers from 1 to n.

Valeric decided to sort the balls in the order of increasing of their numbers by the following scheme. He will put each new ball in the basket with the least number of balls. And if he's got several variants, he chooses the basket which stands closer to the middle. That means that he chooses the basket for which <image> is minimum, where i is the number of the basket. If in this case Valeric still has multiple variants, he chooses the basket with the minimum number.

For every ball print the number of the basket where it will go according to Valeric's scheme.

Note that the balls are sorted into baskets in the order of increasing numbers, that is, the first ball goes first, then goes the second ball and so on.

Input

The first line contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of balls and baskets, correspondingly.

Output

Print n numbers, one per line. The i-th line must contain the number of the basket for the i-th ball.

Examples

Input

4 3


Output

2
1
3
2


Input

3 1


Output

1
1
1

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author pttrung
 */

/*
 * aaaaaaaaa
  
 aaa

 */
public class B {

    public static int Mod = 1000003;

    public static void main(String[] args) throws FileNotFoundException {

        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        int m = in.nextInt();
        Basket[] data = new Basket[m];
        double mid = (double) (m + 1) / 2;
        PriorityQueue<Basket> q = new PriorityQueue();
        for (int i = 0; i < data.length; i++) {
            double point = Math.abs(mid - (i + 1));
            data[i] = new Basket(i + 1,0, point);
            q.add(data[i]);
        }
        
        for (int i = 0; i < n; i++) {
            Basket b = q.poll();
            out.println(b.num);
            b.value += 1;
            q.add(b);
        }
        out.close();
    }

    static class Basket implements Comparable<Basket> {

        int num, value;
        double point;

        public Basket(int num, int value, double point) {
            this.num = num;
            this.value = value;
            this.point = point;
        }

        @Override
        public int compareTo(Basket o) {
            if (value != o.value) {
                return value - o.value;
            } else if (point != o.point) {
                if (point < o.point) {
                    return -1;
                }
                return 1;
            } else {
                return num - o.num;
            }
        }
    }

    public static double solve(double dist, int vp, int vd) {
        return (double) dist / (vd - vp);
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;

        }
    }

    public static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * (val * a);
        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            // br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("square_detector.txt"))));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}