Recursive Formulas - Definition & Examples

Let $f_1$ denote the string "EXPII". The string $f_{k+1}$ is created by inserting the string $\text{EXPII}$ in between each of it's letters. For example,

$$f_2 = \textbf{E}\text{EXPII}\textbf{X}\text{EXPII}\textbf{P}\text{EXPII}\textbf{I}\text{EXPII}\textbf{I}\text{EXPII}$$

where the letters in bold represent $f_1$. What is the $2594^{\text{th}}$ letter of $f_5$?

Source: Lexington Math Tournament