Find the Duplicate Number
<p>Given an array of integers <code>nums</code> containing&nbsp;<code>n + 1</code> integers where each integer is in the range <code>[1, n]</code> inclusive.</p>

<p>There is only <strong>one repeated number</strong> in <code>nums</code>, return <em>this&nbsp;repeated&nbsp;number</em>.</p>

<p>You must solve the problem <strong>without</strong> modifying the array <code>nums</code>&nbsp;and using only constant extra space.</p>

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

<pre>
<strong>Input:</strong> nums = [1,3,4,2,2]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,1,3,4,2]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,3,3,3,3]
<strong>Output:</strong> 3</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>nums.length == n + 1</code></li>
	<li><code>1 &lt;= nums[i] &lt;= n</code></li>
	<li>All the integers in <code>nums</code> appear only <strong>once</strong> except for <strong>precisely one integer</strong> which appears <strong>two or more</strong> times.</li>
</ul>

<p>&nbsp;</p>
<p><b>Follow up:</b></p>

<ul>
	<li>How can we prove that at least one duplicate number must exist in <code>nums</code>?</li>
	<li>Can you solve the problem in linear runtime complexity?</li>
</ul>
Bit Manipulation; Array; Two Pointers; Binary Search
class Solution:
    def findDuplicate(self, nums: List[int]) -> int:
        def f(x: int) -> bool:
            return sum(v <= x for v in nums) > x

        return bisect_left(range(len(nums)), True, key=f)
