IrMO 2014 Problem 5

Suppose $a_1,a_2,\ldots,a_n>0$ , where $n>1$ and $\sum_{i=1}^{n}a_i=1$ . For each $i=1,2,\ldots,n$ , let $b_i=\frac{a^2_i}{\sum\limits_{j=1}^{n}a^2_j}$ . Prove that $$\sum_{i=1}^{n}\frac{a_i}{1-a_i}\le \sum_{i=1}^{n}\frac{b_i}{1-b_i} .$$ When does equality occur ?