Number Clicker

Description:

Input:

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.

Output:

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.

Sample Input:

1 3 5

Sample Output:

2
1 1

Sample Input:

3 2 5

Sample Output:

1
3

Note:

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 $$$3 \to 2$$$.