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Solution: Nth Magical Number

Explore how to find the nth magical number, which is divisible by either of two given integers, without generating the entire sequence. Learn to use binary search combined with the inclusion-exclusion principle and least common multiple calculations for efficient problem-solving. This lesson helps you master counting techniques and optimization strategies for large 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 ...