<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 Solution {
public:
    vector<int> parents;
    vector<int> ranks;
    vector<int> counts;
    vector<int> groupCounts;
    vector<int> cur_string;

    int find(int x) {
        if (parents[x] != x) {
            parents[x] = find(parents[x]);
        }
        return parents[x];
    }

    void union_sets(int x, int y) {
        int r1 = find(x);
        int r2 = find(y);

        groupCounts[counts[r1]]--;
        groupCounts[counts[r2]]--;
        counts[r1] = counts[r2] = counts[r1] + counts[r2];
        groupCounts[counts[r1]]++;

        if (r1 != r2) {
            if (ranks[r1] >= ranks[r2]) {
                parents[r2] = r1;
                if (ranks[r1] == ranks[r2]) {
                    ranks[r1]++;
                }
            } else {
                parents[r1] = r2;
                ranks[r2]++;
            }
        }
    }

    int findLatestStep(vector<int>& arr, int m) {
        int n = arr.size();
        parents = vector<int>(n);
        ranks = vector<int>(n, 0);
        counts = vector<int>(n, 1);
        groupCounts = vector<int>(n + 1, 0);
        cur_string = vector<int>(n, 0);

        for (int i = 0; i < n; i++) {
            parents[i] = i;
        }

        int ans = -1;

        for (int step = 0; step < n; step++) {
            int i = arr[step] - 1;
            groupCounts[1]++;

            if (i > 0 && cur_string[i-1] == 1) {
                union_sets(i, i-1);
            }
            if (i < n-1 && cur_string[i+1] == 1) {
                union_sets(i, i+1);
            }

            cur_string[i] = 1;

            if (groupCounts[m] > 0) {
                ans = step + 1;
            }
        }

        return ans;
    }
};
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