<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 check(self, i, k, cookies, fair):
        if i == len(cookies):
            self.res = min(self.res, max(fair))
            return 
        
        if self.res < max(fair):
            return
            
        for j in range(k):
            fair[j] += cookies[i]
            self.check(i + 1, k, cookies, fair)
            fair[j] -= cookies[i]

        
    def distributeCookies(self, cookies: List[int], k: int) -> int:
        self.res = float('inf')
        self.check(0, k, cookies, [0] * k)
        return self.res
16600