<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) {
       auto parent = vector<int>(arr.size(), -1);
       auto sizes = vector<int>(arr.size());
       auto bitstring = std::string(arr.size(), '0');
       auto numGroups = 0;
       auto latestStep = -1;
       for (int i = 0; i < arr.size(); i++) {
           auto ind = arr[i] - 1;
           auto size = 1;
           bitstring[ind] = '1';
        //    printf("i is %d, ind is %d, bitstring is %s\n", i, ind, bitstring.c_str());
           parent[ind] = ind;
           if (ind - 1 >= 0 && bitstring[ind - 1] == '1') {
               auto parentInd = getParentInd(parent, ind - 1);
               auto leftSize = sizes[parentInd];
            //    printf("parentInd is %d, leftSize is %d\n", parentInd, leftSize);
               if (leftSize == m) {
                   numGroups--;
               }
               size += leftSize;
               parent[parentInd] = ind;
           }
           if (ind + 1 < bitstring.size() && bitstring[ind + 1] == '1') {
               auto parentInd = getParentInd(parent, ind + 1);
               auto rightSize = sizes[parentInd];
            //    printf("parentInd is %d, rightSize is %d\n", parentInd, rightSize);
               if (rightSize == m) {
                   numGroups--;
               }
               size += rightSize;
               parent[parentInd] = ind;
           }
           sizes[ind] = size;
        //    printf("size is %d\n", sizes[ind]);
           if (size == m) {
               numGroups++;
           }
           if (numGroups > 0) {
               latestStep = i + 1;
           }
       }
       return latestStep;
   }


   int getParentInd(vector<int>& parent, int ind) {
       int nextInd = ind;
       while (parent[nextInd] != nextInd) {
            // printf("parentInd is %d, ind is %d\n", parent[ind], ind);
           nextInd = parent[nextInd];
       }
    //    printf("nextInd is %d, ind is %d\n", nextInd, ind);
       return nextInd;
   }
};

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