<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 {
    int n;
    vector<int> size;
    vector<int> parents;

    int _find_root(int node) {
        if (parents[node] == node)
            return node;
        parents[node] = _find_root(parents[node]); // Path compression
        return parents[node];
    }

public:
    DSU(int n) : size(n, 1), parents(n) {
        for(int i = 0; i < n; i++) 
            parents[i] = i;
    };

    // Union -> returns 
    void combine(int node1, int node2) {
        int root1 = _find_root(node1);
        int root2 = _find_root(node2);
        if (root1 == root2) return;

        if (size[root1] < size[root2]) {
            size[root2] += size[root1];
            parents[root1] = root2;
        } else {
            size[root1] += size[root2];
            parents[root2] = root1;
        }
    }

    // Returns 'id' for containing set
    int find(int node) {
        return _find_root(node);
    }

    // Gets the size of the containing set
    int get_size(int node) {
        return size[_find_root(node)];
    }
};

class Solution {
public:
    int findLatestStep(vector<int>& arr, int m) {
        DSU dsu(arr.size());

        vector<bool> seen(arr.size(), false);
        int last = -1;
        for(int i = 0; i < arr.size(); i++) {
            int to_set = arr[i]-1;
            seen[to_set] = true;
            bool was_m = false;
            if (to_set && seen[to_set-1]) {
                was_m = was_m || dsu.get_size(to_set-1) == m;
                dsu.combine(to_set-1, to_set);
            }
            if (to_set+1 < arr.size() && seen[to_set+1]) {
                was_m = was_m || dsu.get_size(to_set+1) == m;
                dsu.combine(to_set, to_set+1);
            }
            if (was_m) last = i;
        }

        return m == arr.size() ? arr.size() : last;
    }
};
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