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 C++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <assert.h>
#include <algorithm>
using namespace std;

bool what[111111];

int main(void)
{
	int n, m, i;

	scanf("%d %d", &n, &m);

	if (n % 2)
	{
		int front = 1, end = n - 1;
		for (i = 1; i <= m; i++)
		{
			printf("%d %d\n", front, end);
			front++, end--;
		}
	}
	else
	{
		int front = 1, end = n;
		for (i = 1; i <= min(n / 4, m); i++)
		{
			printf("%d %d\n", front, end);
			what[front] = what[end] = true;
			front++, end--;
		}

		if (m > n / 4)
		{
			int cnt = 1;
			for (i = n / 4 + 1; i <= m; i++)
			{
				if (what[i] || what[i + cnt * 2 > n ? (i + cnt * 2) % n + 1 : i + cnt * 2])
					continue;
				printf("%d %d\n", i, i + cnt * 2 > n ? (i + cnt * 2) % n + 1 : i + cnt * 2);
				what[i] = what[i + cnt * 2 > n ? (i + cnt * 2) % n + 1 : i + cnt * 2] = true;
				++cnt;
			}
		}
	}
	return 0;
}