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.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.io.InputStream;

public class SolC {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskSolver solver = new TaskSolver();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskSolver {

    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();

        int i = 1;
        int j = k+1;
        while(i <= j) {
            out.print(i + " ");
            if(i != j)
                out.print(j + " ");
            i++;
            j--;
        }

        for (i = k+2; i <= n; i++) {
            out.print(i + " ");
        }

        out.println();
    }

}

/*
    int in.nextInt()
    String in.nextString()

    out.print(n + " ") //must be " " which is a String object.
    out.close()
*/
class InputReader {
    InputStream stream;
    byte[] buf = new byte[1024];
    int curChar, numChars;

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

    private int read() {

        if (numChars == -1)
            throw new InputMismatchException();
        //buffer wraps around here. Hence the buf array size does not matter.
        /*
        if the buffer size is enough, i.e 1024. InputStream load at most 1024 bytes(if necessary)
        into buffer. read() returns 1 byte every time. After the first read, it only needs to
        return corresponding byte in the buf every time it is called. it does not have to call
        input stream to read again.
        Only if the bug has run out does InputReader has to call stream.read(buf) to reload the
        buf.
        */
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }


    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

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

}

class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void println(Object... objects){
        print(objects);
        print("\n");
    }

    public void close() {
        writer.close();
    }

}