Problem 2449. Back to the future II

I've spent much time trying to solve this problem without hacking. After finally giving up and seeing the solution, I can attest it is only possible to solve this problem with hacks. The author last came in Cody servers in 2016, and the p function no longer works. Don't waste unnecessary time trying to solve this through traditional means. You will see what was the trick, and why it no longer works when you hack it.

And let this be a lesson to all people out there. Sometimes problems are just broken. On the internet and in famous textbooks. Although some authors will probably die before admitting they made a mistake. :)