Nth Magical Number

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Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

A positive integer is **magical** if it is divisible by a or by b (or both). Given n, a, and b, return the n-th smallest magical number, counting from 1. Numbers divisible by both a and b appear only once in the sequence. The answer can be huge, so return it modulo 1_000_000_007. Note that you must find the exact n-th number first and only then reduce it; do not compare reduced values.

Examples

Input: n = 1, a = 2, b = 3
Output: 2
The magical numbers are 2, 3, 4, 6, ...; the first is 2.
Input: n = 4, a = 2, b = 3
Output: 6
2, 3, 4, 6: the fourth is 6.
Input: n = 5, a = 2, b = 4
Output: 10
Multiples of 4 are already multiples of 2, so the sequence is 2, 4, 6, 8, 10.

Constraints

  • 1 <= n <= 10^9
  • 2 <= a, b <= 4 * 10^4

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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