There is a group of G members, and a list of various crimes they could commit.
The ith crime generates a 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 P profit, and the total number of members participating in that subset of crimes is at most G.
How many schemes can be chosen?  Since the answer may be very large, return it modulo 10^9 + 7.
 
Example 1:
Input: G = 5, P = 3, group = [2,2], profit = [2,3]
Output: 2
Explanation: 
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: G = 10, P = 5, group = [2,3,5], profit = [6,7,8]
Output: 7
Explanation: 
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).

 

Note:

1 <= G <= 100
0 <= P <= 100
1 <= group[i] <= 100
0 <= profit[i] <= 100
1 <= group.length = profit.length <= 100

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution:\n    def profitableSchemes(self, G: int, P: int, group: List[int], profit: List[int]) -> int:\n        # backpack problem\n        \n        # states: subset of schemes profit[1..i], rest members j.\n        # dp[i][j][k]: number of schemes ending with i, with rest members j, and rest profit k.\n        # transition:  dp[i][j][k] = sum_[l in 1..i-1](dp[l][j+group[j]][k+profit[i]]), k > 0\n        #              dp[i][j][0] = sum_[l in 1..i-1; m in 0..profit[i]-1](dp[l][j+group[i]][m])\n        # boundary: dp[0][G][P] = 1, dp[i][G][k] = 0\n        \n#         dp = [[[0 for _ in range(P+1)] for _ in range(G+1)] for _ in range(len(profit)+1)]\n#         dp[0][-1][-1] = 1\n                \n#         mod = int(1e9+7)\n#         for i in range(1, len(profit)+1):\n#             for j in range(G-group[i-1], -1, -1):\n#                 for k in range(P-profit[i-1], -profit[i-1]-1, -1):\n#                     for l in range(i-1, -1, -1):\n#                         dp[i][j][max(0, k)] = (dp[i][j][max(0, k)] + dp[l][j+group[i-1]][k+profit[i-1]]) % mod\n                        \n#         # print(dp)\n#         res = 0\n#         for i in range(1, len(profit)+1):\n#             for j in range(G+1):\n#                 res = (res + dp[i][j][0]) % mod\n#         return res\n                \n\n# ===================================  \n# O(n^4) will cause TLE.\n        \n        # change k -> at most rest profit k; i -> for 1..i (not ending at)\n        # transition: dp[i][j][k] = dp[i-1][j][k] -> not include profit[i]\n        #                           + dp[i-1][j+group[i]][k+profit[i]] -> include profit[i]\n        # boundary: dp[i][G][P] = 1, dp[i][G][k] = 0.\n        \n        dp = [[[0 for _ in range(P+1)] for _ in range(G+1)] for _ in range(len(profit)+1)]\n        dp[0][-1][-1] = 1\n        # for i in range(len(profit)+1):\n        #     dp[i][-1][-1] = 1\n        \n        mod = int(1e9+7)\n        for i in range(1, len(profit)+1):\n            for j in range(G, -1, -1):\n                for k in range(P, -1, -1):\n                    dp[i][j][k] = dp[i-1][j][k]\n                for k in range(P, -1, -1):\n                    if j + group[i-1] <= G: # feasible\n                        dp[i][j][k] = (dp[i][j][k] + dp[i-1][j+group[i-1]][min(k+profit[i-1], P)]) % mod\n                        \n        # print(dp)\n        res = 0\n        for j in range(G+1):\n            res = (res + dp[-1][j][0]) % mod\n        return res'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'profitableSchemes'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 9068