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.awt.Point;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.AbstractList;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import sun.misc.Queue;

/**
 *
 * @author Mojtaba
 */
public class Main {

    public static void main(String[] args) throws IOException, InterruptedException {
        MojtabaKhooryaniScanner in = new MojtabaKhooryaniScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");

        int n = in.nextInt();
        int k = in.nextInt();
        int num = 1;
        sb.append(num).append(" ");
        int sign = 1;
        int dif = k;
        for (int i = 0; i < k; i++) {
            num += (sign * dif);
            sb.append(num).append(" ");
            dif--;
            sign *= -1;
        }
        for (int i = k + 2; i <= n; i++) {
            sb.append(i).append(" ");
        }

        writer.println(sb.toString());
        writer.close();
        in.close();
    }
}

class MojtabaKhooryaniScanner {

    BufferedReader reader;
    StringTokenizer tokenizer;

    public MojtabaKhooryaniScanner(InputStream stream) {
        this.reader = new BufferedReader(new InputStreamReader(stream));
    }

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

    public int[] nextIntegerArray(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public long[] nextLongArray(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    public int nextInt(int radix) throws IOException {
        return Integer.parseInt(next(), radix);
    }

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

    public long nextLong(int radix) throws IOException {
        return Long.parseLong(next(), radix);
    }

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

    public BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }

    public BigInteger nextBigInteger(int radix) throws IOException {
        return new BigInteger(next(), radix);
    }

    public String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
            return this.next();
        }
        return tokenizer.nextToken();
    }

    public void close() throws IOException {
        this.reader.close();
    }
}
