KMO 2022 Problem 4

For positive integers $m, n$ ( $m>n$ ), $a_{n+1}, a_{n+2}, ..., a_m$ are non-negative integers that satisfy the following inequality. $$2> \frac{a_{n+1}}{n+1} \ge \frac{a_{n+2}}{n+2} \ge \cdots \ge \frac{a_m}{m}$$ Find the number of pair $(a_{n+1}, a_{n+2}, \cdots, a_m)$ .