Hello coders,

Currently, I am stuck with the following problem: Given 2 powers, a[0] ^ (a[1] ^ (a[2] ^ (... ^ a[n]))) and b[0] ^ (b[1] ^ (b[2] ^ (... ^ b[m]))), how to compare these two powers? (a[i], b[i], n, m <= 100)

I believe that there must be some mathematical trick to solve this problem but I could not find out myself. I hope that someone can help me with this. Thank you very much.

Another matter is, I wonder if there is a simple and fast way to compute (a[0] ^ (a[1] ^ (a[2] ^ (... ^ a[n]))) % MOD) for some MOD. All I can think of is to use Euler theorem a ^ totient(MOD) = 1 (% MOD), but it seems pretty low. Can someone help me with this too?

Thank you for your time and consideration. Happy Coding