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Solution: Nth Magical Number

Understand how to determine the nth magical number divisible by either a or b using efficient binary search combined with the inclusion-exclusion principle and least common multiple calculations. This lesson guides you through implementing a solution that avoids explicit sequence generation, ensures optimal time complexity, and applies modular arithmetic 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

  • ...