OMCC 2019 Problem 1

Let $N=\overline{abcd}$ be a positive integer with four digits. We name plátano power to the smallest positive integer $p(N)=\overline{\alpha_1\alpha_2\ldots\alpha_k}$ that can be inserted between the numbers $\overline{ab}$ and $\overline{cd}$ in such a way the new number $\overline{ab\alpha_1\alpha_2\ldots\alpha_kcd}$ is divisible by $N$ . Determine the value of $p(2025)$ .