Leetcode 878. Nth Magical Number

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

Return the N-th 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

Example 3:

Input: N = 5, A = 2, B = 4
Output: 10

Example 4:

Input: N = 3, A = 6, B = 4
Output: 8

Note:

1. 1 <= N <= 10^9
2. 2 <= A <= 40000
3. 2 <= B <= 40000

Code (Java):

class Solution {
    public int nthMagicalNumber(int N, int A, int B) {
        long lo = 2;
        long hi = Long.MAX_VALUE;
        
        while (lo < hi) {
            long mid = lo + (hi - lo) / 2;
            
            long lcm = A * B / gcd(A, B);
            
            long count = mid / A + mid / B - mid / lcm;
            
            if (count < N) {
                lo = mid + 1;
            } else {
                hi = mid;
            }
        }
        
        long module = (long) Math.pow(10, 9) + 7;
        return (int)(lo % module);
    }
    
    private long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        
        return gcd(b, a % b);
    }
}