I have a math problem at school, but i haven't idea how to solve this problem

Given three natural numbers $$$n, a, b$$$. We define a pair $$$(x, y)$$$ as a beautiful pair if it satisfies all the following conditions:

• $$$1 \leq x \leq a$$$
• $$$1 \leq y \leq b$$$
• $$$(x \times y)$$$ is divisible by $$$(x + y)$$$ and the division result does not exceed $$$n$$$.
• $$$x$$$ and $$$y$$$ are natural numbers.

Requirement: Count the number of pairs $$$(x, y)$$$ that satisfy the conditions above and are considered beautiful pairs.

Input

• Contains three natural numbers $$$n, a, b$$$ $$$(1 \leq n, a, b \leq 10^{10})$$$.
• The data ensures that the result of the problem will not exceed $$$10^{18}$$$.

Output

• Print the result after performing the required task.

can you help me how to solve this problem

(I use a translator to write this post, sorry for my bad English)