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Solution: Nth Magical Number

Understand how to solve for the nth magical number, divisible by either a or b, using an efficient binary search algorithm. Explore the use of the inclusion-exclusion principle and least common multiple calculations to count valid numbers within a range, enabling you to tackle similar mathematical coding interview problems with confidence.

Statement

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 109+710^9+7.

Constraints:

  • 11 \leq n 109\leq 10^9

  • 22 \leq a, b 4×104\leq 4 \times 10^4 ...