13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5ee,

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.

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!

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.

Note

In the first example the integer on th

Number Clicker

Examples