409004: GYM103414 H Octopus Game

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 $$$k$$$, 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 $$$10^{18}$$$, otherwise something bad might happen. Those players are winning the round, who get $$$0$$$ written on one of the cards, after performing at most $$$50$$$ actions.

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

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

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 ($$$0 \le n \le 50$$$). Note that you need not minimize the number of actions, but it must not exceed $$$50$$$.

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 $$$10^{18}$$$ by their absolute values.

-3 9

1
2 3

-27 57

2
2 2
1 9

56 15

6
1 -2
1 -1
2 -2
1 1
2 2
1 -4

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 $$$3$$$ on the cards, respectively, after the second action the integers are $$$0$$$ and $$$3$$$.

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