<p>A positive integer is <em>magical</em> if it is divisible by either <code>a</code> or <code>b</code>.</p>

<p>Given the three integers <code>n</code>, <code>a</code>, and <code>b</code>, return the <code>n<sup>th</sup></code> magical number. Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1, a = 2, b = 3
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 4, a = 2, b = 3
<strong>Output:</strong> 6
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>2 &lt;= a, b &lt;= 4 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int nthMagicalNumber(int n, int a, int b) {
        const int MOD = 1e9 + 7;
        long lcm = (long long)a * b / std::gcd(a, b);
        long low = std::min(a, b);
        long high = (long long)n * std::min(a, b);
        while (low < high) {
            long mid = low + (high - low) / 2;
            if (mid / a + mid / b - mid / lcm < n) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low % MOD;
    }
};
7500