AIME 2022b Problem 13

There is a polynomial $P(x)$ with integer coefficients such that$$P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}$$holds for every $0<x<1.$ Find the coefficient of $x^{2022}$ in $P(x)$.