<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>

using ll=long long;
class Solution {
    vector<vector<ll>>dp;
    ll memo(int ind,vector<int>&peep,int skill_mask,int skill_cnt){
        if(skill_mask==(1<<skill_cnt)-1)return 0;
        if(ind>=peep.size())return (1LL<<peep.size())-1LL;
        
        if(dp[skill_mask][ind]!=-1)return dp[skill_mask][ind];

        ll pick=((ll)1<<peep.size())-1;

        int new_mask=skill_mask|peep[ind];

        if(new_mask>skill_mask)pick=(1LL<<ind)| memo(ind+1,peep,new_mask,skill_cnt);
        
        ll not_pick=memo(ind+1,peep,skill_mask,skill_cnt);

        int pop_cnt_pick=__builtin_popcountll(pick);
        int pop_cnt_not_pick=__builtin_popcountll(not_pick);

        return dp[skill_mask][ind]= pop_cnt_pick<pop_cnt_not_pick?pick:not_pick;
    }

public:
    vector<int> smallestSufficientTeam(vector<string>& req_skills, vector<vector<string>>& people) {
        unordered_map<string,int>skill;
        for(int i=0;i<req_skills.size();i++)skill[req_skills[i]]=i;
        int skill_cnt=req_skills.size();
        dp.resize(1<<skill_cnt,vector<ll>(people.size(),-1));
        vector<int>peep(people.size());
        for(int i=0;i<people.size();i++){
            int skill_mask=0;
            for(auto j:people[i]){
                skill_mask |= (1<<skill[j]);
            }
            peep[i]=skill_mask;
        }
        ll person_mask=0;
        ll ans=memo(0,peep,0,skill_cnt);
        vector<int>ans_v;
        for(int i=0;i<64;i++){
            if(ans & (1LL<<i))ans_v.push_back(i);
        }
        return ans_v; 
    }
};
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