Allen is playing Number Clicker on his phone.
He starts with an integer $$$u$$$ on the screen. Every second, he can press one of 3 buttons.
Allen wants to press at most 200 buttons and end up with $$$v$$$ on the screen. Help him!
The first line of the input contains 3 positive integers: $$$u, v, p$$$ ($$$0 \le u, v \le p-1$$$, $$$3 \le p \le 10^9 + 9$$$). $$$p$$$ is guaranteed to be prime.
On the first line, print a single integer $$$\ell$$$, the number of button presses. On the second line, print integers $$$c_1, \dots, c_\ell$$$, the button presses. For $$$1 \le i \le \ell$$$, $$$1 \le c_i \le 3$$$.
We can show that the answer always exists.
1 3 5
3 2 5
In the first example the integer on the screen changes as $$$1 \to 2 \to 3$$$.
In the second example the integer on the screen changes as $$$3 \to 2$$$.