Repeated Calculations

Kaneki and Hide are bored at college, so they decide to play a small game to test how well both of them are at calculating large values. At the beginning of the game, Kaneki picks two numbers $a$ and $b$, and Hide picks two numbers $c$ and $d$. Initially, two numbers, **1000 and 7**, are written on a blackboard (these numbers will always be the first two numbers on the board). When it’s Kaneki’s t