Consider the array `[3,6,9,12]`. If we generate all the combinations with repetition that sum to `12`, we get `5` combinations: `[12], [6,6], [3,9], [3,3,6], [3,3,3,3]`. The length of the sub-arrays (such as `[3,3,3,3]` should be less than or equal to the length of the initial array (`[3,6,9,12]`).  

Given an array of positive integers and a number `n`, count all combinations with repetition of integers that sum to `n`. For example: 
```Haskell
find([3,6,9,12],12) = 5.
```

More examples in the test cases. 

Good luck!

If you like this Kata, please try:

[Array combinations](https://www.codewars.com/kata/59e66e48fc3c499ec5000103)

[Sum of prime-indexed elements](https://www.codewars.com/kata/59f38b033640ce9fc700015b)

```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 = 'import itertools\n\n\n#Given the lst of length N, we generate a list of all possible combinations with\n#  replacements from choose-1 to choose-N\n#Then, for each of the combinations found, simply sum the contents and see if the sum\n#matches the target sum\n# Example [3, 6, 9, 12] with target sum 12. Here we need a total of 4; \n# choose (with replacement) 1 from 4, 2 from 4, 3 from 4, 4 from 4\n# Choose 1 [(3,), (6,), (9,), (12,)]\n# Choose 2 [(3, 3), (3, 6), (3, 9), (3, 12), (6, 6), (6, 9), (6, 12), (9, 9), (9, 12), (12, 12)]\n#           [(3, 3, 3), (3, 3, 6), (3, 3, 9), (3, 3, 12), (3, 6, 6), (3, 6, 9), (3, 6, 12), (3, 9, 9),\n#            (3, 9, 12), (3, 12, 12), (6, 6, 6), (6, 6, 9), (6, 6, 12), (6, 9, 9), (6, 9, 12), \n#            (6, 12, 12), (9, 9, 9), (9, 9, 12), (9, 12, 12), (12, 12, 12)]\n# Choose 3 [(3, 3, 3, 3), (3, 3, 3, 6), (3, 3, 3, 9), (3, 3, 3, 12), (3, 3, 6, 6), (3, 3, 6, 9),\n#           (3, 3, 6, 12), (3, 3, 9, 9), (3, 3, 9, 12), (3, 3, 12, 12), (3, 6, 6, 6), (3, 6, 6, 9),\n#           (3, 6, 6, 12), (3, 6, 9, 9), (3, 6, 9, 12), (3, 6, 12, 12), (3, 9, 9, 9), (3, 9, 9, 12),\n#           (3, 9,12, 12), (3, 12, 12, 12), (6, 6, 6, 6), (6, 6, 6, 9), (6, 6, 6, 12), (6, 6, 9, 9),\n#           (6, 6, 9, 12), (6, 6, 12, 12), (6, 9, 9, 9), (6, 9, 9, 12), (6, 9, 12, 12), (6, 12, 12, 12),\n#           (9, 9, 9, 9), (9, 9, 9, 12), (9, 9, 12, 12), (9, 12, 12, 12), (12, 12, 12, 12)] \n#Now for each we see which sum to the target of 12\ndef find(lst, targetSum):\n    lenList = len(lst)\n    \n\n    combWithReplacementList= []\n    for chooseR in range(1, lenList+1):\n        combsChooseR = itertools.combinations_with_replacement(lst, chooseR)\n        combWithReplacementList.append(list(combsChooseR))\n\n    totalFound = 0\n    for col in combWithReplacementList:\n        for combChoice in col:\n            if (sum(combChoice))== targetSum:\n                totalFound +=1\n\n    return totalFound\n#----end function\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find'
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: 7014