Given an integer array A, and an integer target, return the number of tuples i, j, k  such that i < j < k and A[i] + A[j] + A[k] == target.
As the answer can be very large, return it modulo 109 + 7.
 
Example 1:
Input: A = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Explanation: 
Enumerating by the values (A[i], A[j], A[k]):
(1, 2, 5) occurs 8 times;
(1, 3, 4) occurs 8 times;
(2, 2, 4) occurs 2 times;
(2, 3, 3) occurs 2 times.

Example 2:
Input: A = [1,1,2,2,2,2], target = 5
Output: 12
Explanation: 
A[i] = 1, A[j] = A[k] = 2 occurs 12 times:
We choose one 1 from [1,1] in 2 ways,
and two 2s from [2,2,2,2] in 6 ways.

 
Constraints:

3 <= A.length <= 3000
0 <= A[i] <= 100
0 <= target <= 300

```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 threeSumMulti(self, A: List[int], target: int) -> int:\n        def find_n_sum(arr, target, N, l, r, path, output):\n            if arr[l]*N>target or arr[r]*N<target:\n                return\n            \n            if N==2:\n                s, e = l, r\n                while s<e:\n                    total = arr[s]+arr[e]\n                    if total<target or s>l and arr[s-1]==arr[s]:\n                        s += 1\n                    elif total>target or e<r and arr[e]==arr[e+1]:\n                        e -= 1\n                    else:\n                        output.add(tuple(path+[arr[s], arr[e]]))\n                        s += 1\n                        e -= 1\n            else:\n                for i in range(l, r+1-(N-1)):\n                    if i>l and arr[l]==arr[l-1]:\n                        continue\n                        \n                    find_n_sum(arr, target-arr[i], N-1, i, r, path+[arr[i]], output)\n            \n            \n        combos = set()\n        res = 0\n        counter = Counter(A)\n        new_arr = []\n        for k in sorted(counter.keys()):\n            new_arr += [k]*min(counter[k], 3)\n\n        find_n_sum(new_arr, target, 3, 0, len(new_arr)-1, [], combos)\n        \n        for lst in combos:\n            cnt = 1\n            temp = Counter(lst)\n            for k in temp:\n                for i in range(temp[k]):\n                    cnt *= (counter[k]-i)/(i+1)\n                \n            res = (res+cnt)%(10**9+7)\n            \n        return int(res)%(10**9+7)\n                \n                                                                \n                                                                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'threeSumMulti'
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: 14498