Simple Harmonic (1).

A thin disc of mass $m$ is connected to two ideal, massless springs of spring constants $k_1$ and $k_2,$ using two frictionless axles: one attached to the center of the disc and the other at its topmost point. The friction between the disc and the ground below is sufficient for pure rolling motion. The disc is given a small displacement from its equilibrium position and released. The time period of small oscillations of the disc can be expressed as $T = 2 \pi \sqrt{\dfrac{am}{b(ck_1 + dk_2)}},$ where $(a,b) , (a,c) , (a,d) , (c,d)$ are pairwise coprime positive integers.

Calculate $a+b+c+d$.