<p>There is a group of <code>n</code> members, and a list of various crimes they could commit. The <code>i<sup>th</sup></code> crime generates a <code>profit[i]</code> and requires <code>group[i]</code> members to participate in it. If a member participates in one crime, that member can&#39;t participate in another crime.</p>

<p>Let&#39;s call a <strong>profitable scheme</strong> any subset of these crimes that generates at least <code>minProfit</code> profit, and the total number of members participating in that subset of crimes is at most <code>n</code>.</p>

<p>Return the number of schemes that can be chosen. Since the answer may be very large, <strong>return it modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 5, minProfit = 3, group = [2,2], profit = [2,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong> To make a profit of at least 3, the group could either commit crimes 0 and 1, or just crime 1.
In total, there are 2 schemes.</pre>

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

<pre>
<strong>Input:</strong> n = 10, minProfit = 5, group = [2,3,5], profit = [6,7,8]
<strong>Output:</strong> 7
<strong>Explanation:</strong> To make a profit of at least 5, the group could commit any crimes, as long as they commit one.
There are 7 possible schemes: (0), (1), (2), (0,1), (0,2), (1,2), and (0,1,2).</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>0 &lt;= minProfit &lt;= 100</code></li>
	<li><code>1 &lt;= group.length &lt;= 100</code></li>
	<li><code>1 &lt;= group[i] &lt;= 100</code></li>
	<li><code>profit.length == group.length</code></li>
	<li><code>0 &lt;= profit[i] &lt;= 100</code></li>
</ul>

class Solution:
    def profitableSchemes(self, n: int, minProfit: int, group: List[int], profit: List[int]) -> int:

        dp = {}
        # @cache
        # def helper(n, minProfit, i):
        #     if n < 0:
        #         return 0
            
        #     if i == len(group):
        #         return 0 if minProfit > 0 else 1

        #     if n == 0:
        #         return 0 if minProfit > 0 else 1
                
        #     wish1 = 0
        #     wish1 = helper(n - group[i], minProfit - profit[i], i + 1)
        #     wish2 = helper(n, minProfit, i + 1)

        #     return (wish1 + wish2) % (10 ** 9 + 7)

        # return helper(n, minProfit, 0)

        for i in range(minProfit + 1):
            for j in range(len(group) + 1):
                dp[(0, i, j)] = 0 if i > 0 else 1
        
        for i in range(n + 1):
            for j in range(minProfit + 1):
                dp[(i, j, len(group))] = 0 if j > 0 else 1
        
        for i in range(1, n + 1):
            for j in range(minProfit + 1):
                for k in range(len(group) - 1, -1, -1):
                    dp[(i, j, k)] = dp[(i, j, k + 1)]
                    if i - group[k] >= 0:
                        dp[(i, j, k)] += dp[(i - group[k], max(0, j - profit[k]), k + 1)]
                        dp[(i, j, k)] = dp[(i, j, k)] % (10 ** 9 + 7)
        
        return dp[(n, minProfit, 0)]
        

        

        
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