<p>Given an integer array <code>arr</code>, partition the array into (contiguous) subarrays of length <strong>at most</strong> <code>k</code>. After partitioning, each subarray has their values changed to become the maximum value of that subarray.</p>

<p>Return <em>the largest sum of the given array after partitioning. Test cases are generated so that the answer fits in a <strong>32-bit</strong> integer.</em></p>

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

<pre>
<strong>Input:</strong> arr = [1,15,7,9,2,5,10], k = 3
<strong>Output:</strong> 84
<strong>Explanation:</strong> arr becomes [15,15,15,9,10,10,10]
</pre>

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

<pre>
<strong>Input:</strong> arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4
<strong>Output:</strong> 83
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [1], k = 1
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 500</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= k &lt;= arr.length</code></li>
</ul>

class Solution {
public:
    int solve(int k,int prev,vector<int> nums){
        if(prev>=nums.size())  return 0;
        int ans =0;
        int maxi = 0;
        for(int index= prev;index<prev+k && index<nums.size();index++){
            maxi = max(maxi,nums[index]);
            ans = max(ans, maxi*(index -prev+1) + solve(k,index+1,nums));
        }
        return ans;
    }
    int maxSumAfterPartitioning(vector<int>& nums, int k) {
        // return solve(k,0,nums);  
        vector<int> dp(nums.size()+1,0);
        for(int prev = nums.size()-1;prev>=0;prev--){
            int ans =0;
            int maxi = 0;
            for(int index= prev;index<prev+k && index<nums.size();index++){
                maxi = max(maxi,nums[index]);
                ans = max(ans, maxi*(index -prev+1) +dp[index+1]);
            }
            dp[prev] =  ans;
        }
        return dp[0];
    }
};
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