<p>Given an array <code>arr</code> that represents a permutation of numbers from <code>1</code> to <code>n</code>.</p>

<p>You have a binary string of size <code>n</code> that initially has all its bits set to zero. At each step <code>i</code> (assuming both the binary string and <code>arr</code> are 1-indexed) from <code>1</code> to <code>n</code>, the bit at position <code>arr[i]</code> is set to <code>1</code>.</p>

<p>You are also given an integer <code>m</code>. Find the latest step at which there exists a group of ones of length <code>m</code>. A group of ones is a contiguous substring of <code>1</code>&#39;s such that it cannot be extended in either direction.</p>

<p>Return <em>the latest step at which there exists a group of ones of length <strong>exactly</strong></em> <code>m</code>. <em>If no such group exists, return</em> <code>-1</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [3,5,1,2,4], m = 1
<strong>Output:</strong> 4
<strong>Explanation:</strong> 
Step 1: &quot;00<u>1</u>00&quot;, groups: [&quot;1&quot;]
Step 2: &quot;0010<u>1</u>&quot;, groups: [&quot;1&quot;, &quot;1&quot;]
Step 3: &quot;<u>1</u>0101&quot;, groups: [&quot;1&quot;, &quot;1&quot;, &quot;1&quot;]
Step 4: &quot;1<u>1</u>101&quot;, groups: [&quot;111&quot;, &quot;1&quot;]
Step 5: &quot;111<u>1</u>1&quot;, groups: [&quot;11111&quot;]
The latest step at which there exists a group of size 1 is step 4.
</pre>

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

<pre>
<strong>Input:</strong> arr = [3,1,5,4,2], m = 2
<strong>Output:</strong> -1
<strong>Explanation:</strong> 
Step 1: &quot;00<u>1</u>00&quot;, groups: [&quot;1&quot;]
Step 2: &quot;<u>1</u>0100&quot;, groups: [&quot;1&quot;, &quot;1&quot;]
Step 3: &quot;1010<u>1</u>&quot;, groups: [&quot;1&quot;, &quot;1&quot;, &quot;1&quot;]
Step 4: &quot;101<u>1</u>1&quot;, groups: [&quot;1&quot;, &quot;111&quot;]
Step 5: &quot;1<u>1</u>111&quot;, groups: [&quot;11111&quot;]
No group of size 2 exists during any step.
</pre>

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

<ul>
	<li><code>n == arr.length</code></li>
	<li><code>1 &lt;= m &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= n</code></li>
	<li>All integers in <code>arr</code> are <strong>distinct</strong>.</li>
</ul>

class DSU:
    def __init__(self, n):
        self.parents = [i for i in range(n + 1)]
        self.size = [1 for i in range(n + 1)]
        self.n = n

    def find(self, v):
        currParent = self.parents[v]
        if currParent == v:
            return v
        parent = self.find(currParent)
        self.parents[v] = parent
        return parent
    
    def union(self, x, y):
        p1, p2 = self.find(x), self.find(y)
        s1, s2 = self.size[p1], self.size[p2]

        if p1 == p2:
            return False

        if s1 > s2:
            self.parents[p2] = p1
            self.size[p1] += s2
        else:
            self.parents[p1] = p2
            self.size[p2] += s1
        return True

class Solution:
    def findLatestStep(self, arr: List[int], m: int) -> int:
        n = len(arr)
        dsu = DSU(n)

        ans = -1
        buckets = set()
        binary = [0 for i in range(n + 1)]

        for i in range(n):
            changed = arr[i]
            binary[changed] = 1

            if changed > 1 and binary[changed - 1]:
                hisParent = dsu.find(changed - 1)
                if hisParent in buckets:
                    buckets.remove(hisParent)
                dsu.union(changed, changed - 1)
                
            if changed < n and binary[changed + 1]:
                hisParent = dsu.find(changed + 1)
                if hisParent in buckets:
                    buckets.remove(hisParent)
                dsu.union(changed, changed + 1)

            nowParent = dsu.find(changed)
            parentSize = dsu.size[nowParent]
            if parentSize == m:
                buckets.add(nowParent)
            if len(buckets) != 0:
                ans = i + 1
            # print(f'after processing {i}, binary: {binary[1:]}, parents: {dsu.parents[1:]}, buckets: {buckets}')
            # print(f'hence answer: {ans}')
        return ans
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