P4902 Product

A problem by CYJian after multiple rounds of strengthening.

Given $A, B$, find the value of the following expression: $$\prod_{i=A}^{B}\prod_{j=1}^{i}\left(\frac{i}{j}\right)^{\left\lfloor \frac{i}{j} \right\rfloor}\bmod 19260817$$ There are $T$ queries. ------ It is said that many people cannot understand the formula. Alright, here is the pseudocode: ``` for i = A to B for j = 1 to i res = res * power(i / j, floor(i / j)) res = solve(res) ``` The final `solve` means converting it into the form of a fraction modulo. It is not guaranteed that the precision will not blow up on the spot.

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

Output $T$ lines. Each line contains one positive integer, the answer for that query.

Sample explanation: $1 \times 4 \times 1 \times 27 \times \frac{3}{2} \times 1 \equiv 162 \pmod{19260817}$. **This problem uses bundled tests.** | Constraints | $T =$ | $A \le B \le$ | |:-:|:-:|:-:| | $1 \sim 5$ | $1$ | $5000$ | | $6 \sim 10$ | $1$ | $10^6$ | | $11 \sim 15$ | $10^6$ | $5000$ | | $16 \sim 20$ | $10^6$ | $10^6$ | Translated by ChatGPT 5