Problem:
Score : 500 points

Problem Statement

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

Sample Input 1

4 1

Sample Output 1

2 3

Let us call the four players A, B, C, and D, and assume that they are initially given the integers 1, 2, 3, and 4, respectively.

The 1-st round is fought by B and C, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 2, 3, 4, and 1, respectively.

The 2-nd round is fought by A and B, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 3, 4, 1, and 2, respectively.

The 3-rd round is fought by D and A, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 4, 1, 2, and 3, respectively.

The 4-th round is fought by C and D, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 1, 2, 3, and 4, respectively.

No player fights the same opponent more than once during the four rounds, so this solution will be accepted.

Sample Input 2

7 3

Sample Output 2

1 6
2 5
3 4

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

public class Main implements Runnable
{
//    static int dx[]={-1,0,1,0};
//    static int dy[]={0,-1,0,1};
    static long mod=1000000007;
    
    public static void main(String[] args) {        
        new Thread(null, new Main(), "", 200 * 1024 * 1024).start();        
    }

    public void run() {
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        
        int n=sc.nextInt();
        int m=sc.nextInt();
        boolean u[]=new boolean[n+1];
        u[1]=u[2]=true;
        out.println(1+" "+2);
        for (int i = 1,a=1,b=2; i < m; i++) {
        	while(u[a])a++;
        	b=a+i+1;
        	while(u[a]||u[b]){a++;b++; if(a>n)a=1;if(b>n)b=1;}
        	u[a]=u[b]=true;
            out.println(a+" "+b);
		}
        out.println();
     	out.flush();
    }
    

    static void ret(String ans) {
    	System.out.println(ans);
    	System.exit(0);
    }

    static void ret(long ans) {
    	System.out.println(ans);
    	System.exit(0);
    }
    
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
}

//class P {
//	int x,c;long s;
//	P(int  x, int c, long s) {
//	  this.x=x;
//	  this.c=c;
//	  this.s=s;
//	}
//}


class P implements Comparable<P>{
	int x,c;long s;
	P(int  x, int c, long s) {
	  this.x=x;
	  this.c=c;
	  this.s=s;
	}

    public int compareTo(P p){
        return Long.signum(s-p.s);
    }
}

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString()
    {
        while( st==null || !st.hasMoreTokens() )
			try {
				st = new StringTokenizer(x.readLine());
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        return st.nextToken();
    }
    public int nextInt()
    {
        return Integer.parseInt(nextString());
    }
    public int[] nextIntArray(int size) {
        int r[] = new int[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextInt(); 
        }
        return r;
    }
    public long[] nextLongArray(int size) {
        long r[] = new long[size];
        for (int i = 0; i < size; i++) {
            r[i] = this.nextLong(); 
        }
        return r;
    }
    public char[] getCharSet() {
        return this.nextString().toCharArray();
    }    
    public long nextLong()
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}