A circular platform of mass M and radius R rotates about a fixed pivot at its center with an initial angular velocity ω. A boy of mass m initially standing at the edge of the platform jumps off the platofrm with a veloctiy v with respect to the ground. What is the new angular velocity of the platform?

(A) ((M+2m)ωR-2mv)/MR
(B) ((M-2m)ωR-2mv)/MR
(C) ((M+2m)ωR+2mv)/MR
(D) ((M+2m)ωR-2mv/R
(E) ((M+2m)ωR-2mv/M