<p>In an infinite binary tree where every node has two children, the nodes are labelled in row order.</p>

<p>In the odd numbered rows (ie., the first, third, fifth,...), the labelling is left to right, while in the even numbered rows (second, fourth, sixth,...), the labelling is right to left.</p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/06/24/tree.png" style="width: 300px; height: 138px;" /></p>

<p>Given the <code>label</code> of a node in this tree, return the labels in the path from the root of the tree to the&nbsp;node with that <code>label</code>.</p>

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

<pre>
<strong>Input:</strong> label = 14
<strong>Output:</strong> [1,3,4,14]
</pre>

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

<pre>
<strong>Input:</strong> label = 26
<strong>Output:</strong> [1,2,6,10,26]
</pre>

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

<ul>
	<li><code>1 &lt;= label &lt;= 10^6</code></li>
</ul>

class Solution:
    def pathInZigZagTree(self, label: int) -> List[int]:
        def gen():
            nonlocal label
            lv, q = 0, label
            yield label
            while q:
                q, r = divmod(q, 2)
                lv += (q > 0)
            real_parent = label
            for i in range(lv - 1, -1, -1):
                original_parernt = label // 2
                offset = abs(original_parernt - 2 ** (i + 1)) - 1
                real_parent = 2 ** i + offset
                yield real_parent
                label = real_parent

        return list(gen())[::-1]
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