<p>You are given an integer array <code>cookies</code>, where <code>cookies[i]</code> denotes the number of cookies in the <code>i<sup>th</sup></code> bag. You are also given an integer <code>k</code> that denotes the number of children to distribute <strong>all</strong> the bags of cookies to. All the cookies in the same bag must go to the same child and cannot be split up.</p>

<p>The <strong>unfairness</strong> of a distribution is defined as the <strong>maximum</strong> <strong>total</strong> cookies obtained by a single child in the distribution.</p>

<p>Return <em>the <strong>minimum</strong> unfairness of all distributions</em>.</p>

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

<pre>
<strong>Input:</strong> cookies = [8,15,10,20,8], k = 2
<strong>Output:</strong> 31
<strong>Explanation:</strong> One optimal distribution is [8,15,8] and [10,20]
- The 1<sup>st</sup> child receives [8,15,8] which has a total of 8 + 15 + 8 = 31 cookies.
- The 2<sup>nd</sup> child receives [10,20] which has a total of 10 + 20 = 30 cookies.
The unfairness of the distribution is max(31,30) = 31.
It can be shown that there is no distribution with an unfairness less than 31.
</pre>

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

<pre>
<strong>Input:</strong> cookies = [6,1,3,2,2,4,1,2], k = 3
<strong>Output:</strong> 7
<strong>Explanation:</strong> One optimal distribution is [6,1], [3,2,2], and [4,1,2]
- The 1<sup>st</sup> child receives [6,1] which has a total of 6 + 1 = 7 cookies.
- The 2<sup>nd</sup> child receives [3,2,2] which has a total of 3 + 2 + 2 = 7 cookies.
- The 3<sup>rd</sup> child receives [4,1,2] which has a total of 4 + 1 + 2 = 7 cookies.
The unfairness of the distribution is max(7,7,7) = 7.
It can be shown that there is no distribution with an unfairness less than 7.
</pre>

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

<ul>
	<li><code>2 &lt;= cookies.length &lt;= 8</code></li>
	<li><code>1 &lt;= cookies[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= k &lt;= cookies.length</code></li>
</ul>

class Solution:
    def distributeCookies(self, cookies: List[int], k: int) -> int:
        memory = {}
        distribution = [0] * k
        self.res = float("inf")

        # Parameters:
        # start: Integer -> From what numbered bag to start looking for.
        # c: Integer -> Which kid number we are currently distributing the cookies to.
        # mask: Integer -> The (atmost 8 bit) bitmask indicating which bags are up for grabs.
        # curr_cookies: Integer -> Tells how many cookies have been given to child 'c' so far.
        def aux(start, c, mask, curr_cookies):
            # Trivials
            if(c == k):
                all_1s = (1 << len(cookies)) - 1
                if(mask & all_1s == all_1s):
                    self.res = min(self.res, max(distribution))
                    return
                else:
                    return
            
            for i in range(start, len(cookies)):
                if(mask & (1 << i) == 0):
                    if(i < len(cookies) - 1):
                        aux(i + 1, c, mask | (1 << i), curr_cookies + cookies[i])
                    distribution[c] = curr_cookies + cookies[i]
                    aux(0, c + 1, mask | (1 << i), 0)
                    distribution[c] = 0

        aux(0, 0, 0, 0)
        return self.res
        
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