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Nth Magical Number

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

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

Given the three integers n, a, and b, return the nth magical number. Since the answer may be very large, return it modulo 10^9 + 7.

Example 1

Input: n = 1, a = 2, b = 3

Output: 2

Example 2

Input: n = 4, a = 2, b = 3

Output: 6

Constraints

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

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