IMC 2016 Problem 6

Let $(x_1,x_2,\ldots)$ be a sequence of positive real numbers satisfying ${ \sum_{n=1}^{\infty}\frac{x_n}{2n-1}=1}$ . Prove that $$\sum_{k=1}^{\infty} \sum_{n=1}^{k} \frac{x_n}{k^2} \le2.$$ (Proposed by Gerhard J. Woeginger, The Netherlands)