<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>

set<int>s;
class DSU{
    public:
    vector<int>size,parent;
    
    int k;
    DSU(int n,int m)
    {
        size.resize(n+1,1);
        parent.resize(n+1,0);
        for(int i=1;i<=n;i++)
        parent[i]=i;
        k=m;
    }
    int find_par(int u)
    {
        if(u==parent[u])
        return u;
        return parent[u]=find_par(parent[u]);
    }
    void Merge(int u,int v)
    {
        u=find_par(u);
        v=find_par(v);
        if(u==v)
        {
           if(size[u]==k)s.insert(u);
            return; 
        }
        if(size[u]<size[v])
        swap(u,v);

        size[u]+=size[v];
        parent[v]=u;
        if(size[u]==k)
        {
            s.insert(u);
        }
        else{
            if(size[v]==k)
            {
                if(s.find(v)!=s.end())
            s.erase(s.find(v));
            }
            if(s.find(u)!=s.end())
            s.erase(s.find(u));
        }

    }
};
class Solution {
public:

    int findLatestStep(vector<int>& a, int m) 
    {
        int n=a.size();
        int st=-1;
       DSU dt(n,m);
       s.clear();
       vector<int>vis(n+2,0);
       for(int i=0;i<n;i++)
       {
        // cout<<i<<endl;
        int el=a[i];
        vis[el]=1;
        dt.Merge(el,el);
        if(el<n && vis[el+1])
        dt.Merge(el,el+1);
        if(el>1 && vis[el-1])
        dt.Merge(el,el-1);
        // cout<<dt.s.size()<<endl;
        if(s.size()>=1)
        st=i+1;
       }
       return st;
    }
};
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