E. Number Clickertime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAllen 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.  Turn u \to u+1 \pmod{p}.  Turn u \to u+p-1 \pmod{p}.  Turn u \to u^{p-2} \pmod{p}. Allen wants to press at most 200 buttons and end up with v on the screen. Help him!InputThe 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.OutputOn 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.ExamplesInput1 3 5Output21 1Input3 2 5Output13NoteIn 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. 
Input1 3 5
Output21 1
['divide and conquer', 'graphs', 'meet-in-the-middle', 'number theory', '*2700']