Distribution of a ratio built from normal samples

Let $X_1,X_2,…,X_m,Y_1,…,Y_n$ be i.i.d. $N(0,1)$ random variables. Then

$$W=\frac{n\left(\sum_{i=1}^mX_i\right)^2}{m\left(\sum_{j=1}^nY_j^2\right)}$$

has