**Profitable Schemes ** There is a group of `n`

members, and a list of various crimes they could commit. The `i`

crime generates a ^{th}`profit[i]`

and requires `group[i]`

members to participate in it. If a member participates in one crime, that member can’t participate in another crime.

Let’s call a **profitable scheme** any subset of these crimes that generates at least `minProfit`

profit, and the total number of members participating in that subset of crimes is at most `n`

.

Return the number of schemes that can be chosen. Since the answer may be very large, **return it modulo** `10`

.^{9} + 7

**Example 1:**

Input:n = 5, minProfit = 3, group = [2,2], profit = [2,3]Output:2Explanation: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.

**Example 2:**

Input:n = 10, minProfit = 5, group = [2,3,5], profit = [6,7,8]Output:7Explanation: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).

**Constraints:**

`1 <= n <= 100`

`0 <= minProfit <= 100`

`1 <= group.length <= 100`

`1 <= group[i] <= 100`

`profit.length == group.length`

`0 <= profit[i] <= 100`

### Profitable Schemes Solutions

✅**Time:** O(n)

✅**Space:** O(n)

**C**++

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