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.math.BigInteger;
public class Main
{
	public static  void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		// String h[]=sc.nextLine().split(" ");
		// long n=Long.parseLong(sc.nextLine());
		String s[]=sc.nextLine().split(" ");
		long a=Long.parseLong(s[0]);
		long b=Long.parseLong(s[1]);
		StringBuilder sb=new StringBuilder();
		// int j=1;
		for(int i=1;i<=b;i++)
		{
			sb.append(i+" "+(a-i+1)+"\n");
		
		}
		System.out.print(sb);
	}
	static int get(int [] arr, int k, int i, ArrayList<Pair>ch, int m)
	{
		if(i==arr.length)
		{
			int sum=0;
			for(int u=0;u<ch.size();u++)
			{
				if(arr[ch.get(u).b-1]-arr[ch.get(u).a-1]==ch.get(u).c){sum+=ch.get(u).d;}
			}
			return sum;
		}
		int max=0;
		for(int u=k;u<=m;u++)
		{
			arr[i]=u;
			max=Math.max(max,get(arr,u,i+1,ch,m));
			
		}
		return max;
	}

}
class Pair
{
	int a;
	int b;
	int c;
	int d;
	Pair(int e,int f, int g,int h){
		a=e;
		b=f;
		c=g;
		d=h;
	}
}