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Solution: Nth Magical Number

Discover how to determine the nth magical number defined as a positive integer divisible by either of two given integers. Explore the use of binary search combined with the inclusion-exclusion principle and the least common multiple to optimize finding this number. This lesson helps you develop an efficient approach to solve large numerical problems while managing computational constraints.

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 ...