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Nth Magical Number (hard)

Problem Statement

Given the three integers n, a, and b, return the n<sup>th</sup> magical number modulo 10^9 + 7 as it can be very large.

A positive integer is called magical if it is divisible by either a or b.

Examples

  • Example 1:

    • Input: n = 3, a = 2, b = 3
    • Expected Output: 4
    • Justification: The first three magical numbers divisible by 2 or 3 are 2, 3, and 4. The third magical number is 4.

  • Example 2:

    • Input: n = 5, a = 3, b = 4
    • Expected Output: 9

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