<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 {
private:
    struct UnionFind {
        struct Node {
            Node() {}
            Node(int x) : val(x) {}
            int val;
            int group_size{0};
        };
        std::vector<Node> parent;
        int desired_size;
        int num_desired_size;
        UnionFind(int n, int group_size) : parent(n + 1), desired_size(group_size), num_desired_size(0) {
            std::iota(parent.begin(), parent.end(), 0);
        }
        int Find(int x) {
            if (x != parent[x].val)
                parent[x] = Find(parent[x].val);
            return parent[x].val;
        }
        void Union(int x, int y) {
            int p_x = Find(x), p_y = Find(y);
            if (p_x != p_y) {
                if (parent[p_y].group_size == desired_size)
                    --num_desired_size;
                parent[p_x].group_size += parent[p_y].group_size;
                parent[p_y] = parent[p_x];
            }
        }
        void set_true(int x) {
            parent[x].group_size = 1;
            if (x > 0 && parent[x-1].group_size > 0) Union(x, x-1);
            if (x < parent.size() - 1 && parent[x+1].group_size > 0) Union(x, x+1);
            if (desired_size == parent[x].group_size) ++num_desired_size;
        }
        bool has_desired_size() const { return num_desired_size > 0; }
    };
public:
    int findLatestStep(vector<int>& arr, int m) {
        int n = arr.size(), res = -1;
        UnionFind ufs(n, m);
        std::vector<int> visualize(n + 1, 0);
        for (int i = 0; i < n; ++i) {
            visualize[arr[i]] = 1;
            ufs.set_true(arr[i]);
            if (ufs.has_desired_size()) res = i + 1;
        }
        return res;
    }
};
88600