24850번 - Octopus Game 스페셜 저지다국어

문제

The tournament of "Octopus Game" is held in some country.

This round the participants will deal with math puzzle. Each player has two cards, initially there are integers $a_0$ and $b_0$ at the cards, respectively.

Players make actions with their cards. Let the integers on player's cards be $a$ and $b$. The player first chooses an integer $k,ドル and then performs one of the following operations:

1. replace the integer on the first card with $a + kb$;
2. replace the integer on the second card with $b + ka$.

While playing, the absolute value of an integer written on a card must not exceed 10ドル^{18},ドル otherwise something bad might happen. Those players are winning the round, who get 0ドル$ written on one of the cards, after performing at most 50ドル$ actions.

You are going to play the game, and of course you would like to win!

입력

The only line of input contains two integers $a_0$ and $b_0$ --- the initial integers written on the cards ($-10^{18} \le a_0, b_0 \le 10^{18}$).

출력

The first line must contain $n$ --- the number of actions that the player is willing to perform to get 0 on one of the cards (0ドル \le n \le 50$). Note that you need not minimize the number of actions, but it must not exceed 50ドル$.

The following $n$ lines must contain two space separated integers each: $t_i$ and $k_i$ --- the type of the respective action and the chosen integer $k$.

If there are multiple valid solutions, it is allowed to output any of them, but note that during the game the integers on the cards must not exceed 10ドル^{18}$ by their absolute values.

제한

노트

The first test requires just one action: add three times integer on the first card to the integer on the second card.

The second test: after the first action there are integers $-27$ and 3ドル$ on the cards, respectively, after the second action the integers are 0ドル$ and 3ドル$.

The third test: the integers on the cards are in turn: 56ドル$ and 15ドル,ドル 26ドル$ and 15ドル,ドル 11ドル$ and 15ドル,ドル 11ドル$ and $-7,ドル 4ドル$ and $-7,ドル 4ドル$ and 1ドル,ドル 0ドル$ and 1ドル$.