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 $\leq 4 \times 10^4$

To find the nth number divisible by either a or b, we observe that magical numbers form a sorted sequence of all multiples of a and b. Instead of generating this sequence explicitly, we can efficiently count how many magical numbers are $\leq x$ using the inclusion-exclusion principle:

• Count of numbers divisible by a: $\lfloor x / a \rfloor$ ...