Chess Tournament

시간 제한2초메모리 제한512 MB

요약

n명이 서로 한 번씩 대결하는 리그전에서 한 라운드에 최대 k개의 경기만 동시에 진행할 수 있을 때, 모든 대진을 마치는 최소 라운드 수와 그 일정을 출력한다.

난이도: 보통10점 중 7점
유형: 조합론, 그리디, 구현, 수학
정답자: 아직 제출이 없습니다

문제

Alex organizes a chess tournament in his company. The tournament is a round-robin tournament of $n$ people, and each pair of players will face each other exactly once.

The problem is, there are only $k$ chess boards in the office ( $k \le \frac{n}{2}$ ). So only $k$ games can be played at the same time. Let's call $g$ games, being simultaneously played by $2g$ distinct players, where $1 \le g \le k$ , a round.

Your task is to help Alex to set a schedule with a minimal number of rounds.

입력

The input contains two integers $n$ and $k$ ( $2 \le n \le 200, 1 \le k \le \frac{n}{2}$ ) --- the number of players and the number of chess boards.

출력

In the first line output an integer $r$ --- the number of rounds.

Then output $r$ sections, describing rounds. In the first line of each section, output an integer $g$ ( $1 \le g \le k$ ) --- the number of games in this round. Then output $g$ lines with two integers each --- the pairs of players that will play in this round. All these $2g$ integers must be distinct integers from $1$ to $n$ .

If there are several possible solutions, output any of them.

예제3

예제 1
입력
```
4 2
```
예상 출력
```
3
2
2 3
1 4
2
2 4
3 1
2
1 2
3 4
```

예제 2

입력

5 2

예상 출력

예제 3

입력

6 2

예상 출력