Concatenation of Consecutive Binary Numbers
<p>Given an integer <code>n</code>, return <em>the <strong>decimal value</strong> of the binary string formed by concatenating the binary representations of </em><code>1</code><em> to </em><code>n</code><em> in order, <strong>modulo </strong></em><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
<strong>Output:</strong> 1
<strong>Explanation: </strong>&quot;1&quot; in binary corresponds to the decimal value 1. 
</pre>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 27
<strong>Explanation: </strong>In binary, 1, 2, and 3 corresponds to &quot;1&quot;, &quot;10&quot;, and &quot;11&quot;.
After concatenating them, we have &quot;11011&quot;, which corresponds to the decimal value 27.
</pre>

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

<pre>
<strong>Input:</strong> n = 12
<strong>Output:</strong> 505379714
<strong>Explanation</strong>: The concatenation results in &quot;1101110010111011110001001101010111100&quot;.
The decimal value of that is 118505380540.
After modulo 10<sup>9</sup> + 7, the result is 505379714.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>
Bit Manipulation; Math; Simulation
class Solution:
    def concatenatedBinary(self, n: int) -> int:
        mod = 10**9 + 7
        ans = 0
        for i in range(1, n + 1):
            ans = (ans << i.bit_length() | i) % mod
        return ans
