<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:
    def nthMagicalNumber(self, n: int, a: int, b: int) -> int:
        MOD = 10**9 + 7
        lcm = a/gcd(a, b) * b
        def PIE(x):
            return x//a + x//b - x//lcm
        lo, hi = 0, n * min(a, b)
        while lo < hi:
            mid = lo + (hi - lo) // 2
            if PIE(mid) < n:
                lo = mid + 1
            else:
                hi = mid
        return lo % MOD
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