Given three integers n, a, and b, return the nth magical number.

A magical number is defined as a positive integer that is divisible by either a or b.

As the result may be very large, return it modulo $10^9+7$.

Constraints:

• $1 \leq$ n $\leq 10^9$

• $2 \leq$ a, b $\leq 4 \times 10^4$

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.