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.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	static int n, m;
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		m = sc.nextInt();
		sc.close();

		boolean ret = exec(n - 1);
		if (!ret) {
			exec(n - 2);
		}
	}

	static boolean exec(int start) {
		boolean[] used = new boolean[n + 1];
		Set<Integer> set = new HashSet<>();
		int cnt = 0;
		int j = start;
		List<String> list = new ArrayList<>(m);
		for (int i = 1; i <= n; i++) {
			if (used[i]) {
				continue;
			}
			for ( ; j >= 0; j--) {
				if (j == 0) {
					j = n - 1;
				}
				if (set.contains(j)) {
					continue;
				}
				int i2 = i + j;
				int i3 = i + n;
				if (i2 > n) {
					i2 -= n;
					i3 -= n;
				}
				if (used[i2]) {
					continue;
				}
				if (!set.contains(i3 - i2)) {
					set.add(j);
					set.add(i3 - i2);
					used[i] = true;
					used[i2] = true;
					list.add(i + " " + i2);
					cnt++;
					if (cnt == m) {
						PrintWriter pw = new PrintWriter(System.out);
						for (int k = 0; k < m; k++) {
							pw.println(list.get(k));
						}
						pw.flush();
						return true;
					}
					break;
				}
			}
		}
		return false;
	}
}