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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;

class Program {
    public struct Vec2Dint {
        public int x;
        public int y;

        public Vec2Dint (int _x, int _y) {
            x = _x;
            y = _y;
        }
    }

    static void Main (string[] args) {
        string[] S = Console.ReadLine ().Split (' ');
        int N = int.Parse (S[0]);
        int M = int.Parse (S[1]);

        HashSet<int> used = new HashSet<int> ();
        for (int i = 0; i < N; i++) {
            used.Add (i);
        }
        Vec2Dint[] arena = new Vec2Dint[M];
        for (int i = 0; i < M; i++) {
            bool found = false;
            int now = i;
            while (!found) {
                if (used.Contains (now) && used.Contains (now + i + 1)) {
                    found = true;
                    used.Remove (now);
                    used.Remove (now + i + 1);
                } else if (used.Contains (now) && used.Contains ((now + i + 1) % N)) {
                    found = true;
                    used.Remove (now);
                    used.Remove ((now + i + 1) % N);
                } else {
                    now++;
                    now %= N;
                }
            }
            arena[i] = new Vec2Dint (now, now + i + 1);
        }

        foreach (Vec2Dint vector in arena) {
            Console.Write (vector.x + 1);
            Console.Write (" ");
            Console.WriteLine (vector.y + 1);
        }
    }
}