RU-SPB 2016 Problem 102

Given the positive numbers $x_1, x_2,..., x_n$ , such that $x_i \le 2x_j$ with $1 \le i < j \le n$ . Prove that there are positive numbers $y_1\le y_2\le...\le y_n$ , such that $x_k \le y_k \le 2x_k$ for all $k=1,2,..., n$