<p>You are given an integer array <code>jobs</code>, where <code>jobs[i]</code> is the amount of time it takes to complete the <code>i<sup>th</sup></code> job.</p>

<p>There are <code>k</code> workers that you can assign jobs to. Each job should be assigned to <strong>exactly</strong> one worker. The <strong>working time</strong> of a worker is the sum of the time it takes to complete all jobs assigned to them. Your goal is to devise an optimal assignment such that the <strong>maximum working time</strong> of any worker is <strong>minimized</strong>.</p>

<p><em>Return the <strong>minimum</strong> possible <strong>maximum working time</strong> of any assignment. </em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> jobs = [3,2,3], k = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> By assigning each person one job, the maximum time is 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> jobs = [1,2,4,7,8], k = 2
<strong>Output:</strong> 11
<strong>Explanation:</strong> Assign the jobs the following way:
Worker 1: 1, 2, 8 (working time = 1 + 2 + 8 = 11)
Worker 2: 4, 7 (working time = 4 + 7 = 11)
The maximum working time is 11.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= jobs.length &lt;= 12</code></li>
	<li><code>1 &lt;= jobs[i] &lt;= 10<sup>7</sup></code></li>
</ul>

subset = [[] for _ in range(1<<12)]
for mask in range(1<<12):
    s = mask
    while s>0:
        subset[mask].append(s)
        s=(s-1)&mask

class Solution:
    def minimumTimeRequired(self, jobs: List[int], k: int) -> int:
        n = len(jobs)
        u = (1<<n)-1
        dp = [[inf]*(k+1) for _ in range(1<<n)]
        s= [0]*(1<<n)
        for i, v in enumerate(jobs):
            bit = 1 << i
            for j in range(bit):
                s[bit | j] = s[j] + v



        # for mask in range(1<<n):
        #     for i in range(n):
        #         if mask & 1<<i: s[mask]+=jobs[i]
        for mask in range(1<<n):
            for i in range(1,k+1):
                if i==1: dp[mask][i]=s[mask]
                for g in subset[mask]:
                    ne = dp[mask^g][i-1] if dp[mask^g][i-1]>s[g] else s[g]
                    if ne<dp[mask][i]: dp[mask][i]=ne

        return dp[u][k]
            



        
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