$\min_{p_i} \sum_{i=1}^{N} \frac{p_i}{r_i (1 - \frac{ap_i}{r_i})} s.t. \sum_{p_i}^{N} = 1 $

Question

$$\min_{p_i} \sum_{i=1}^{N} \frac{p_i}{r_i (1 - \frac{ap_i}{r_i})}$$ $$s.t. \sum_{i=1}^{N} p_i= 1 $$ where $a \in \mathbb{R}$, $r_i \in \mathbb{R}$ $\forall i$ , $p_i > 0$, $r_i>a p_i$

I tried to solve it using Lagrangian method, but could not find the result.