Picard Groups of Some Quot Schemes

Let C be a smooth projective curve over the field of complex numbers C of genus $g(C)>0$. Let E be a locally free sheaf on C of rank r and degree e. Let Q:=Quot_C/C(E,k,d) denote the Quot scheme of quotients of E of rank k and degree d. For $k>0$ and d 0, we compute the Picard group of Q.