PDF of product of two complex Gaussian random variables?

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I am trying to find the PDF of product of two i.i.d complex Gaussian random variables say $X\sim \mathcal{C}{N}(0,\sigma^2_x)$ and $Y\sim \mathcal{C}{N}(0,\sigma^2_y)$ but not getting it exactly.

Any help in this regard will be highly appreciated.