Nemotron-IMO-Bench 2026 C17

Let $p$ be a prime number. A flea is at point $0$ of the real line. At each minute, the flea has three possibilities: to stay at its position, or to move by $1$ to the left or to the right. After $p-1$ minutes, it wants to be at $0$ again. If $f(p)$ is number of its strategies to do this, find $f(p)$ modulo $p$.