<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:
        store_dict = {}
        def compute(arr, k):
            if tuple(arr) in store_dict:
                return store_dict[arr]
            if len(arr) == 1:
                new = [0 for _ in range(k)]
                new[0] = arr[0]
                return [new]
            result = compute(arr[1:], k)
            new = [None for _ in range(k * len(result))]
            for i in range(len(result)):
                for j in range(k):
                    a = [result[i][p] for p in range(k)] 
                    a[j] += arr[0]
                    new[k * i + j] = a
            store_dict[tuple(arr)] = new
            return new
        ans = compute(cookies, k) 
        return max(min(ans, key = lambda x : max(x)))
            

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