<p>In a project, you have a list of required skills <code>req_skills</code>, and a list of people. The <code>i<sup>th</sup></code> person <code>people[i]</code> contains a list of skills that the person has.</p>

<p>Consider a sufficient team: a set of people such that for every required skill in <code>req_skills</code>, there is at least one person in the team who has that skill. We can represent these teams by the index of each person.</p>

<ul>
	<li>For example, <code>team = [0, 1, 3]</code> represents the people with skills <code>people[0]</code>, <code>people[1]</code>, and <code>people[3]</code>.</li>
</ul>

<p>Return <em>any sufficient team of the smallest possible size, represented by the index of each person</em>. You may return the answer in <strong>any order</strong>.</p>

<p>It is <strong>guaranteed</strong> an answer exists.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> req_skills = ["java","nodejs","reactjs"], people = [["java"],["nodejs"],["nodejs","reactjs"]]
<strong>Output:</strong> [0,2]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> req_skills = ["algorithms","math","java","reactjs","csharp","aws"], people = [["algorithms","math","java"],["algorithms","math","reactjs"],["java","csharp","aws"],["reactjs","csharp"],["csharp","math"],["aws","java"]]
<strong>Output:</strong> [1,2]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= req_skills.length &lt;= 16</code></li>
	<li><code>1 &lt;= req_skills[i].length &lt;= 16</code></li>
	<li><code>req_skills[i]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>req_skills</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= people.length &lt;= 60</code></li>
	<li><code>0 &lt;= people[i].length &lt;= 16</code></li>
	<li><code>1 &lt;= people[i][j].length &lt;= 16</code></li>
	<li><code>people[i][j]</code> consists of lowercase English letters.</li>
	<li>All the strings of <code>people[i]</code> are <strong>unique</strong>.</li>
	<li>Every skill in <code>people[i]</code> is a skill in <code>req_skills</code>.</li>
	<li>It is guaranteed a sufficient team exists.</li>
</ul>

#define ll long long 
#define REP(i,a,n)for(int i=a;i<n;i++)
#define f first
#define sec second 
class Solution {
public:
    ll func(ll i,ll mask,vector<vector<ll>>&dp,ll n,vector<vector<string>>&p,unordered_map<string,ll>&m)
    {
        if(mask==0)return 0;
        if(i==n)return 1e18;
        if(dp[i][mask]!=-1)return dp[i][mask];
        ll notpick=func(i+1,mask,dp,n,p,m);
        ll init=mask;
        for(auto e:p[i])
        {
            ll ind=m[e];
            if(mask&(1<<ind))mask^=(1<<ind);
        }
        ll pick=1+func(i+1,mask,dp,n,p,m);
        return dp[i][init]=min(notpick,pick);
    }
    vector<int> smallestSufficientTeam(vector<string>& sk, vector<vector<string>>& people) {
        unordered_map<string,ll>m;
        REP(i,0,sk.size())m[sk[i]]=i;
        ll numskills=sk.size();
        ll n=people.size();
        vector<vector<ll>>dp(n,vector<ll>(1<<numskills,-1));
        vector<int>ans;
        ll i=0;
        ll mask=(1<<numskills)-1;
        while((i<n)&&(mask!=0))
        {
        ll notpick=func(i+1,mask,dp,n,people,m);
        ll init=mask;
        for(auto e:people[i])
        {
            ll ind=m[e];
            if(mask&(1<<ind))mask^=(1<<ind);
        }
        ll pick=1+func(i+1,mask,dp,n,people,m); 
        if(pick<=notpick)ans.push_back(i);
        else mask=init;
        i++;
        }
        return ans;
    }
};
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