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Solution: Nth Magical Number

Explore an efficient method to compute the nth magical number divisible by either a or b. Understand how to apply the inclusion-exclusion principle combined with binary search to handle large constraints without generating sequences explicitly, and implement the solution with modulo operations for large results.

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

  • ...