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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

const Main = input => {
  const [ N, M ] = input.split(' ').map(e => Number(e));
  const A = [];
  const n = new Array(N).fill(false);
  const dif = new Set();
  //console.log(dif);

  for(let index=0; index<M; index++) {
    let prefix_i = 0;
    let i, j, cur_dif;    

    do {
      i = n.indexOf(false, prefix_i);
      let prefix_j = i + 1;
      do {
        j = n.indexOf(false, prefix_j);
        cur_dif = j - i;
        //console.log(i, j, cur_dif, dif.has(cur_dif))
        if(!dif.has(cur_dif) || j===N-1) break;
        prefix_j = j + 1;
      } while(true)
      if(!dif.has(cur_dif) || i===N-2) break;
      prefix_i = i + 1;
    } while(true)

    //console.log(`ans: ${i+1} ${j+1}`)
    dif.add(cur_dif);
    A.push(`${i+1} ${j+1}`)
    n[i] = true; n[j] = true;
  }

  console.log(A.join('\n'));
};

Main(require('fs').readFileSync('/dev/stdin', 'utf8').trim());
/*Main(`4 1`);
Main(`7 3`)*/