How to understand the definition of Greedy Target-based Statistics in the CatBoost paper

There is a method named Target statistics to deal with categorical features in the catboost paper. I still some confusion about the mathematical form. Could you some guys to expain how to compute it!

$$ \hat{x}^i_k = \frac{\sum^{p-1}_{j=1}[x_{\sigma_{j},k}=x_{\sigma_p,k}]Y_{\sigma_j}+a\cdot P}{\sum^{p-1}_{j=1}[x_{\sigma_{j},k}=x_{\sigma_p,k}]+a}$$