March Break 2024 - Problem 13

Every minute a snake crawls f(y) in the x direction and g(x) in the y direction (note the input and output are switched) where f(y)=191y+194, and g(x)=194x+191. Starting at (0,0), the snake will be on (m,n) after 179 minutes. Let z be the remainder of m when divided by 179\cdot191. Compute the remainder when z is divided by 179.