Anagram Day

Who among the LKSh students doesn't love anagrams? They are a fun way to play with names, surnames, city names, and more. However, the chipmunk Sergey prefers experimenting with his favorite sequences of non-negative integers. To do this, he first needs to convert each sequence into a string using a straightforward algorithm:

Suppose the sequence $a$ has length $n$. A prime number $p$ is chosen such that n < p \leq 30000 and 26 < p. Define a function $f(k)$ for $k$ from $1$ to $n$. Sergey always selects $p$ so that 0 \leq f(k) \leq 26 for all $k$ from $1$ to $n$. Then, the values f(1), f(2), \ldots, f(n) are calculated sequentially. The resulting function values 1,\ldots,26 correspond to the letters of the Latin alphabet a,\ldots,z, while $0$ corresponds to the symbol '*'. These symbols are appended to an initially empty string $s$ after each calculation of the function value $f(k)$.

Sergey asserts that from the resulting string $s$ and the number $p$, the original sequence $a$ can always be reconstructed. Can you do it?