Marinada '23

[lang=hr] Neka je $b_k$ eksponent uz $2$ u kanonskom rastavu broja $k!$. Odredi minimalan $k$ takav da je $k-b_k=2023$. Kako odgovor može biti velik, ispišite ostatak pri dijeljenju tog broja s $47$. [/lang] [lang=en] Let $b_k$ be exponent of $2$ in prime factorization of $k!$. Find the least $k$ such that $k-b_k=2023$. Since the result might be large, write the remainder when $k$ is divided by $47$. [/lang]