<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:
    int findLatestStep(vector<int>& arr, int m) {
        if (m > arr.size()) {
            return -1;
        }
        std::unordered_map<int, int> group_len_count;
        std::unordered_map<int, int> left2right_edges;
        std::unordered_map<int, int> right2left_edges;

        int step = 0;
        int latest_step = -1;
        for (const int index : arr) {
            ++step;
            bool connect_to_left = index > 0 && right2left_edges.find(index - 1) != right2left_edges.end();
            bool connect_to_right = index < arr.size() && left2right_edges.find(index + 1) != left2right_edges.end();
            int total_len = 1;
            int left = index;
            int right = index;
            if (connect_to_left) {
                left = right2left_edges[index - 1];
                const int left_len = index - left;
                --group_len_count[left_len];
                total_len += left_len;
                right2left_edges.erase(right2left_edges.find(index - 1));
                if (left_len == m && group_len_count[left_len] == 0) {
                    latest_step = step - 1;
                }
            }

            if (connect_to_right) {
                right = left2right_edges[index + 1];
                const int right_len = right - index;
                --group_len_count[right_len];
                total_len += right_len;
                left2right_edges.erase(left2right_edges.find(index + 1));
                if (right_len == m && group_len_count[right_len] == 0) {
                    latest_step = step - 1;
                }
            }

            right2left_edges[right] = left;
            left2right_edges[left] = right;
            if (total_len == m) {
                latest_step = step;
            }
            if (group_len_count.find(total_len) == group_len_count.end()) {
                group_len_count[total_len] = 0;
            }
            ++group_len_count[total_len];
        }
        return latest_step;
    }
};
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