<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>

class Solution:
    def smallestSufficientTeam(self, req_skills: List[str], people: List[List[str]]) -> List[int]:
        n,m = len(req_skills),len(people)
        skills = {skill:ind for ind,skill in enumerate(req_skills)}
        people_skills = [0]*m
        all_skill = 0
        SMAX = (1<<n); PMAX = (1<<m)
        for ind,p in enumerate(people):
            for skill in p:
                people_skills[ind] |= (1<<skills[skill])
                all_skill |= (1<<skills[skill])
        if all_skill!=SMAX-1: return [-1] # Solution doesnt exists
        dp = [-1]*SMAX
        def solve(mask,index):
            if mask==0: return 0
            if index<0: return PMAX-1
            # print(mask,index)
            if dp[mask]==-1:
                new_mask = (mask|people_skills[index])^people_skills[index]
                # print("I AM INSIDE",mask,index)
                res1 = solve(new_mask,index-1)|(1<<index)
                res2 = solve(mask,index-1)
                # print("INSIDE ",mask,index, res1,res2)
                if res1.bit_count()<res2.bit_count():
                    ans = res1
                else:
                    ans = res2
                dp[mask] = ans
            # print("FINAL DP",mask,index,dp[mask][index])
            return dp[mask]
        res = solve(SMAX-1,m-1)
        ans = []
        for ind,p in enumerate(people):
            if((res>>ind)&1):
                ans.append(ind)
        # print(dp)
        return ans
19987