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.File;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.Scanner;
import java.util.Stack;

public class Main {

    public static void main(String[] args) throws IOException {
        //Scanner in = new Scanner(System.in);
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder();

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

        out.println(sb.toString().trim());
        out.close();
    }

    static class Algorithm {

        static class ArithmeticProgression {

            static long Term(int n, int[] a, int m, long d) {
                return a[m] + (n - m) * d;
            }

            static long Term(int n, long[] a, int m, long d) {
                return a[m] + (n - m) * d;
            }
        }

        static class MyString {

            static int NumberOfIterations(String str, String p) {
                int sum = 0;

                int index = 0;
                while (true) {
                    int temp = str.substring(index).indexOf(p);
                    if (temp >= 0) {
                        index += (temp + p.length());
                        sum++;
                    } else {
                        break;
                    }
                }

                return sum;
            }
        }

        static HashSet<Integer> NumbersFrom(String digitsString) {
            int[] digits = new int[10];
            for (int i = digitsString.length() - 1; i >= 0; i--) {
                if (digitsString.charAt(i) >= '0' && digitsString.charAt(i) <= '9') {
                    digits[digitsString.charAt(i) - '0']++;
                }
            }
            return NumbersFrom(digits);
        }

        static HashSet<Integer> NumbersFrom(int[] digits) {
            int maxDigit = 0;
            for (int i = 0; i < digits.length; i++) {
                maxDigit += digits[i];
            }
            return NumbersFrom(digits, maxDigit);
        }

        static HashSet<Integer> NumbersFrom(int[] digits, int maxDigit) {
            ArrayList<Integer> list = new ArrayList<Integer>();
            for (int i = 0; i < digits.length; i++) {
                if (digits[i] > 0) {
                    list.add(i);
                }
            }
            int t1 = 0;
            int t2 = list.size();
            for (int i = 1; i < maxDigit; i++) {
                for (int j = t1; j < t2; j++) {
                    int number = list.get(j);
                    int temp = number;
                    while (temp > 0) {
                        digits[temp % 10]--;
                        temp /= 10;
                    }

                    for (int k = 0; k < 10; k++) {
                        if (digits[k] > 0) {
                            list.add(number * 10 + k);
                        }
                    }
                    while (number > 0) {
                        digits[number % 10]++;
                        number /= 10;
                    }
                }
                t1 = t2;
                t2 = list.size();
            }
            HashSet<Integer> set = new HashSet<Integer>(list);

            return set;
        }

        static long Exchange(long price, long[] array, boolean remainderAllowed) {
            return Exchange(price, array, true, remainderAllowed);
        }

        static long Exchange(long price, long[] array, boolean sorted, boolean remainderAllowed) {
            if (!sorted) {
                Arrays.sort(array);
            }
            long coins = 0;
            for (int i = array.length - 1; i >= 0 && price > 0; i--) {
                price -= array[i];
                coins++;
            }
            if (remainderAllowed) {
                if (price <= 0) {
                    return coins;
                } else {
                    return 0;
                }
            } else {
                if (price == 0) {
                    return coins;
                } else {
                    return 0;
                }
            }
        }

        static long Exchange(long price, int[] array, boolean remainderAllowed) {
            return Exchange(price, array, true, remainderAllowed);
        }

        static long Exchange(long price, int[] array, boolean sorted, boolean remainderAllowed) {
            if (!sorted) {
                Arrays.sort(array);
            }
            long coins = 0;
            for (int i = array.length - 1; i >= 0 && price > 0; i--) {
                price -= array[i];
                coins++;
            }
            if (remainderAllowed) {
                if (price <= 0) {
                    return coins;
                } else {
                    return 0;
                }
            } else {
                if (price == 0) {
                    return coins;
                } else {
                    return 0;
                }
            }
        }

        static long C(int n, int r) {
            if (r < n / 2) {
                return C(n, n - r);
            }
            return ZarbeMotevali(r + 1, n) / Fact(n - r);
        }

        private static long ZarbeMotevali(int first, int end) {
            long answer = 1;
            for (long i = first; i <= end; i++) {
                answer *= i;
            }
            return answer;
        }

        private static long Fact(int n) {
            return ZarbeMotevali(2, n);
        }

        static int GCD(int m, int n) {
            if (n > m) {
                return GCD(n, m);
            }
            if (m % n == 0) {
                return n;
            }
            return GCD(n, m % n);
        }

        static long GCD(long m, long n) {
            if (n > m) {
                return GCD(n, m);
            }
            if (m % n == 0) {
                return n;
            }
            return GCD(n, m % n);
        }

        static boolean IsPrime(long a) {
            if (a < 2) {
                return false;
            }
            if (a > 2 && a % 2 == 0) {
                return false;
            }
            long temp = (long) Math.sqrt(a);
            for (long i = 3; i <= temp; i += 2) {
                if (a % i == 0) {
                    return false;
                }
            }
            return true;
        }
    }
}

class Graph {

    private int[][] matrix;
    private boolean[] visited;
    private Stack<Integer> DFS;

    public Graph(int[][] matrix) {
        this.matrix = matrix;
        this.DFS = new Stack<Integer>();
        this.visited = new boolean[matrix.length];
    }

    public Stack<Integer> getDFS() {
        this.DFS(0);
        return DFS;
    }

    public Stack<Integer> getDFS(int vertex) {
        this.DFS.clear();
        this.DFS(vertex);
        return this.DFS;
    }

    private void DFS(int vertrx) {
        this.DFS.push(vertrx);
        this.visited[vertrx] = true;

        for (int i = 0; i < this.matrix[vertrx].length; i++) {
            if (this.matrix[vertrx][i] != 0 && !this.visited[i] && vertrx != i) {
                this.DFS(i);
            }
        }
    }
}

class FastScanner {

    private InputStream stream;
    private byte[] buffer = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
    }

    int read() {
        if (numChars == -1) {
            throw new InputMismatchException();
        }
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0) {
                return -1;
            }
        }
        return buffer[curChar++];
    }

    boolean isWhiteSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    boolean isEndline(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

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

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

    float nextFloat() {
        return Float.parseFloat(next());
    }

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

    String next() {
        int c = read();
        while (isWhiteSpaceChar(c)) {
            c = read();
        }
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isWhiteSpaceChar(c));
        return res.toString();
    }

    String nextLine() {
        int c = read();
        while (isEndline(c)) {
            c = read();
        }
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndline(c));
        return res.toString();
    }
}