<p>There is a <strong>hidden</strong> integer array <code>arr</code> that consists of <code>n</code> non-negative integers.</p>

<p>It was encoded into another integer array <code>encoded</code> of length <code>n - 1</code>, such that <code>encoded[i] = arr[i] XOR arr[i + 1]</code>. For example, if <code>arr = [1,0,2,1]</code>, then <code>encoded = [1,2,3]</code>.</p>

<p>You are given the <code>encoded</code> array. You are also given an integer <code>first</code>, that is the first element of <code>arr</code>, i.e. <code>arr[0]</code>.</p>

<p>Return <em>the original array</em> <code>arr</code>. It can be proved that the answer exists and is unique.</p>

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

<pre>
<strong>Input:</strong> encoded = [1,2,3], first = 1
<strong>Output:</strong> [1,0,2,1]
<strong>Explanation:</strong> If arr = [1,0,2,1], then first = 1 and encoded = [1 XOR 0, 0 XOR 2, 2 XOR 1] = [1,2,3]
</pre>

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

<pre>
<strong>Input:</strong> encoded = [6,2,7,3], first = 4
<strong>Output:</strong> [4,2,0,7,4]
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>4</sup></code></li>
	<li><code>encoded.length == n - 1</code></li>
	<li><code>0 &lt;= encoded[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= first &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def decode(self, encoded: List[int], first: int) -> List[int]:
        decoded = []
        for enc in encoded:
            decoded.append(first)
            first ^= enc

        decoded.append(first)

        return decoded

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