Problem: You are going to hold a competition of one-to-one game called AtCoder Janken. (Janken is the Japanese name for Rock-paper-scissors.) N players will participate in this competition, and they are given distinct integers from 1 through N. The arena has M playing fields for two players. You need to assign each playing field two distinct integers between 1 and N (inclusive). You cannot assign the same integer to multiple playing fields. The competition consists of N rounds, each of which proceeds as follows:

* For each player, if there is a playing field that is assigned the player's integer, the player goes to that field and fight the other player who comes there.
* Then, each player adds 1 to its integer. If it becomes N+1, change it to 1.



You want to ensure that no player fights the same opponent more than once during the N rounds. Print an assignment of integers to the playing fields satisfying this condition. It can be proved that such an assignment always exists under the constraints given.

Constraints

* 1 \leq M
* M \times 2 +1 \leq N \leq 200000

Input

Input is given from Standard Input in the following format:


N M


Output

Print M lines in the format below. The i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.


a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print M lines in the format below. The i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.


a_1 b_1
a_2 b_2
:
a_M b_M

Examples

Input

4 1


Output

2 3


Input

7 3


Output

1 6
2 5
3 4

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.io.InputStream;
import java.io.FileInputStream;
import java.util.HashMap;
import java.util.Random;
import java.util.List;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.FileNotFoundException;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/C2";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        int n = in.nextInt();
        int m = in.nextInt();
        if (n % 2 == 1) {
            for (int i = 1; i <= m; i++) {
                System.out.println(i + " " + (n - i + 1));
            }
        } else {
            int cnt = 0;
            int c11 = (n / 2) / 2;
            int c12 = c11 + 1;
            while (cnt < m && c11 > 0) {
                System.out.println(c11 + " " + c12);
                c11--;
                c12++;
                cnt++;
            }
            int c21 = (n / 2) + n / 4;
            int c22 = c21 + 2;
            while (cnt < m) {
                System.out.println(c21 + " " + c22);
                c21--;
                c22++;
                cnt++;
            }
        }
        // 1 2 3 4 5 6 7 8 9 10 11 12 13 14
    }

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }
}

class GcjUtil {
    public static String format(final int x, final String s) {
        return "Case #" + x + ": " + s;
    }
}


class FastScanner {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
        // stream = new FileInputStream(new File("dec.in"));
    }

    int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        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 boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

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

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

    public int[] nextIntArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = nextInt();

        return array;
    }

    public int[][] nextIntMap(int n, int m) {
        int[][] map = new int[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextIntArray(m);
        }
        return map;
    }

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

    public long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nextLong();

        return array;
    }

    public long[][] nextLongMap(int n, int m) {
        long[][] map = new long[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextLongArray(m);
        }
        return map;
    }

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

    public double[] nextDoubleArray(int n) {
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nextDouble();

        return array;
    }

    public double[][] nextDoubleMap(int n, int m) {
        double[][] map = new double[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextDoubleArray(m);
        }
        return map;
    }

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

    public String[] nextStringArray(int n) {
        String[] array = new String[n];
        for (int i = 0; i < n; i++)
            array[i] = next();

        return array;
    }

    public 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();
    }

    public int[][] nextPackedIntArrays(int packN, int size) {
        int[][] res = new int[packN][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < packN; j++) {
                res[j][i] = nextInt();
            }
        }
        return res;
    }
}