Holiday Contest 2025 - Team Round - Problem 15

Consider an array \mathcal{S}, where f(\mathcal{S}) represents the sum of all elements in it. Initially, \mathcal{S} = \{1, 1\}. In each move, you can either add the last element of \mathcal{S} or f(\mathcal{S}) to the back of \mathcal{S}. Determine the minimum number of moves required to make f(\mathcal{S}) = 2024.