Balanced Triangular Loop in Magnetic Field

An equilateral triangular loop of mass $M$ and side $a$ at rest is under the influence of magnetic field B and gravitational field as shown in figure.

If the frame is slightly displaced in downward direction, the time period of small oscillations is given by

$2\pi \sqrt{\dfrac{\sqrt{X}a}{Yg}}$

Find $X+Y$

Details and assumptions

$l = \frac{\sqrt{3}a}{4}$

$g$ is acceleration due to gravity