<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 {
public:
    int distributeCookies(vector<int>& tasks, int K) {
        int n = tasks.size();
        vector<vector<int>> dp((1<<n),vector<int>(K,0));
        vector<int> sum((1<<n),0);
        for(int i = 1;i<(1<<n);i++){
            int s = 0,p = 1;
            for(int j = 0;j<n;j++){
                if(p&i)
                s += tasks[j];
                p *= 2;
            }
            sum[i] = s;
        }
        for(int k = 0;k < K;k ++){
            for(int i = 1;i<(1<<n);i++){
                if(!k){
                    dp[i][k] = sum[i];
                    continue;
                }
                int ans = INT_MAX;
                for(int j = 1;j<=i;j++){
                  if(((j^i)|j) == i){
                    ans = min(ans,max(dp[j][0],dp[(i^j)][k - 1]));
                  }
                }
                dp[i][k] = ans;
            }
            

        }
        // for(auto x : dp){
        //     for(auto y : x)
        //      cout<<y<<" ";
        //      cout<<endl;
        // }
        
       return dp[(1<<n) - 1][K - 1];
    }
};
9000