Olympiad fun number theory (extended euclidean algorithm)

[Proraks]

If [tex]\frac{2017!}{5^{502}}=22\pmod{25}[/tex] and if [tex]2^{502}=4\pmod{25}[/tex] ,

then what is [tex]\frac{2017!}{5^{502}\cdot 2^{502}}\pmod{25}[/tex], by Extended Euclidean Algorithm or by other techniques.