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.util.*;
import java.io.*;
public class a {
public static void main(String[] args) throws IOException
{
    boolean[] sieve = new boolean[1000001];
    Arrays.fill(sieve, true);
    sieve[0]=sieve[1]=false;
    for(int i = 2; i<sieve.length; i++) if(sieve[i]) for(long j = (long)i*i; j<sieve.length; j+=i) sieve[(int)j] = false;
    //Scanner input = new Scanner(new File("input.txt"));
    //PrintWriter out = new PrintWriter(new File("output.txt"));
    PrintWriter out = new PrintWriter(System.out);
    input.init(System.in);
    int n = input.nextInt(), m = input.nextInt();
    ArrayList<Integer> sorted = new ArrayList<Integer>();
    if(m%2 == 0)
    {
        sorted.add((m/2));
        sorted.add(m/2+1);
        for(int i = 0;i<n; i++)
        {
            int a = m/2 - i-1, b = m/2+1+i+1;
            if(a>0)
            {
                sorted.add(a);
                sorted.add(b);
            }
            else
                break;
        }
    }
    else
    {
        sorted.add(m/2+1);
        for(int i = 0; i<n; i++)
        {
            int a = m/2+1-i-1, b = m/2+1+i+1;
            if(a>0)
            {
                sorted.add(a);
                sorted.add(b);
            }
            else
                break;
        }
    }
    for(int i = 0; i<n; i++)
    {
        out.println(sorted.get(i%m));
    }
    out.close();
}

public static long gcd(long a, long b)
{
if(b == 0) return a;
return gcd(b, a%b);
}
public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}
static class IT
{
    int[] left,right, val, a, b;
    IT(int n)
    {
        left = new int[3*n];
        right = new int[3*n];
        val = new int[3*n];
        a = new int[3*n];
        b = new int[3*n];
        init(0,0, n);
    }
    int init(int at, int l, int r)
    {
        a[at] = l;
        b[at] = r;
        if(l==r)
            left[at] = right [at] = -1;
        else 
        {
            int mid = (l+r)/2;
            left[at] = init(2*at+1,l,mid);
            right[at] = init(2*at+2,mid+1,r);
        }
        return at++;
    }
    //return the sum over [x,y]
    int get(int x, int y)
    {
        return go(x,y, 0);
    }
    int go(int x,int y, int at)
    {
        if(at==-1) return 0;
        if(x <= a[at] && y>= b[at]) return val[at];
        if(y<a[at] || x>b[at]) return 0;
        return go(x, y, left[at]) + go(x, y, right[at]);
    }
    //add v to elements x through y
    void add(int x, int y, int v)
    {
        go3(x, y, v, 0);
    }
    void go3(int x, int y, int v, int at)
    {
        if(at==-1) return;
        if(y < a[at] || x > b[at]) return;
        val[at] += (Math.min(b[at], y) - Math.max(a[at], x) + 1)*v;
        go3(x, y, v, left[at]);
        go3(x, y, v, right[at]);
    }
}
}