<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 {
public:
    int mod=1e9+7;
    long long f(int ind,int pro,int n,vector<int>&group, vector<int>&profit,
         vector<vector<vector<long long>>>&dp){
        if(ind<0){
            if(pro<=0) return 1;
            return 0;
        }
        if(dp[ind][pro][n]!=-1) return dp[ind][pro][n]%mod;
        long long p=0,np=0;
        np=f(ind-1,pro,n,group,profit,dp)%mod;
        if(n>=group[ind]){
            p=f(ind-1,max(0,pro-profit[ind]),n-group[ind],group,profit,dp)%mod;
        }
        return dp[ind][pro][n]= (p+np)%mod;
    }
    int profitableSchemes(int n, int minProfit, vector<int>& group, vector<int>& profit) {
        int s=group.size();
        vector<vector<vector<long long>>>dp
            (s,vector<vector<long long>>(minProfit+1,vector<long long>(n+1,-1)));
        return f(s-1,minProfit,n,group,profit,dp)%mod;
    }
};
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