<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>

# State(members, profit, crimes_idx) : 100 * 100 * 100 = 1e6
# Transitions:
# 1. Skip crime: (members, profit, crimes_idx + 1)
# 2. Commit crime: (members - currentMembers, profit + currentProfit, crimes_idx + 1)
MODULO = int(1e9 + 7)

class Solution:
    def calculateSchemes(self, members: int, profit: int, idx: int, min_profit: int, groups: list[int], profits: list[int], dp_dict: dict()) -> int:
        if idx == len(groups):
            return 1 if profit >= min_profit else 0
        state = (members, profit, idx)
        if state in dp_dict:
            return dp_dict[state]
        
        # Skip crime
        dp_dict[state] = self.calculateSchemes(members, profit, idx+1, min_profit, groups, profits, dp_dict)
        # Commit crime
        if members >= groups[idx]:
            dp_dict[state] = (dp_dict[state] + self.calculateSchemes(
                members - groups[idx], min(100, profit + profits[idx]), idx+1, min_profit, groups, profits, dp_dict
            )) % MODULO
        # Return total answer
        return dp_dict[state]
    
    def profitableSchemes(self, n: int, min_profit: int, groups: list[int], profits: list[int]) -> int:
        dp_dict = dict()
        return self.calculateSchemes(n, 0, 0, min_profit, groups, profits, dp_dict)
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