Rigid uniform Rod 'AB' of mass 'M' and Length 'L' is pulled slightly ( Gently ) at the bottom at time t=0 . when it just reaches the horizontal ground. Then Velocities of End's Point's .

$\displaystyle{ V }_{ A }=\sqrt { \cfrac { a }{ b } (gL) } \\ \\ { V }_{ B }=\sqrt { \cfrac { c }{ d } (gL) }$.

Then Find The Value of $a+b+c+d$

**details and Assumptions**

$\bullet$ All Surfaces are Perfectly Smooth.

$\bullet$ Rod May not Necessarily remain always in contact with Vertical wall.

$\bullet$ $a,b,c,d$ all are positive integers , $gcd(a,b)=1$ , $gcd(c,d)=1$