P4900 Cafeteria.

Even if I, CYJian, were to die, die outside, or jump off from here, I would still not eat a single bite of cafeteria food. $$\color{white}\text{So tasty..}$$

On day $i$, the cafeteria has $i$ dishes. CYJian thinks the tastiness of the $j$-th dish on day $i$ is $\left\{\dfrac{i}{j}\right\}$ (where $\{\}$ means taking the fractional part). Of course, CYJian is someone who likes to try things, so he will eat a little of every dish. Now CYJian has $T$ queries. Each query asks for the total tastiness gained from day $A _ i$ to day $B _ i$. Please help him compute it. Output the answer modulo $998244353$.

The first line contains an integer $T$. The next $T$ lines each contain two integers, representing $A$ and $B$ for each query.

Output $T$ lines, each containing a positive integer representing the sum of tastiness. If the answer can be written as $\dfrac{P}{Q}$, then you need to find any $x$ such that $Q \times x \equiv P \pmod{998244353}$, and output $x \bmod 998244353$.

### Sample Explanation On day 1 the tastiness is $0.00$. On day 2 the tastiness is $0.00+0.00=0.00$. On day 3 the tastiness is $0.00+0.50+0.00=0.50$. Thus $0.00+0.00+0.50=0.50=\dfrac{1}{2}$. Since $499122177 \times 2 \equiv 1 \pmod{998244353}$, the answer is $499122177$. ### Constraints **This problem uses bundled testdata.** | Subtask Range | $T =$ | $A \le B \le$ | |:-:|:-:|:-:| | $1 \sim 5$ | $1$ | $5000$ | | $6 \sim 10$ | $1$ | $10^6$ | | $10 \sim 15$ | $10^6$ | $5000$ | | $16 \sim 20$ | $10^6$ | $10^6$ | Translated by ChatGPT 5