Given an array of integers cost and an integer target. Return the maximum integer you can paint under the following rules:

The cost of painting a digit (i+1) is given by cost[i] (0 indexed).
The total cost used must be equal to target.
Integer does not have digits 0.

Since the answer may be too large, return it as string.
If there is no way to paint any integer given the condition, return "0".
 
Example 1:
Input: cost = [4,3,2,5,6,7,2,5,5], target = 9
Output: "7772"
Explanation:  The cost to paint the digit '7' is 2, and the digit '2' is 3. Then cost("7772") = 2*3+ 3*1 = 9. You could also paint "977", but "7772" is the largest number.
Digit    cost
  1  ->   4
  2  ->   3
  3  ->   2
  4  ->   5
  5  ->   6
  6  ->   7
  7  ->   2
  8  ->   5
  9  ->   5

Example 2:
Input: cost = [7,6,5,5,5,6,8,7,8], target = 12
Output: "85"
Explanation: The cost to paint the digit '8' is 7, and the digit '5' is 5. Then cost("85") = 7 + 5 = 12.

Example 3:
Input: cost = [2,4,6,2,4,6,4,4,4], target = 5
Output: "0"
Explanation: It's not possible to paint any integer with total cost equal to target.

Example 4:
Input: cost = [6,10,15,40,40,40,40,40,40], target = 47
Output: "32211"

 
Constraints:

cost.length == 9
1 <= cost[i] <= 5000
1 <= target <= 5000

```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 largestNumber(self, cost: List[int], target: int) -> str:\n        '''dp = [0]\n        for i in range(1,target+1):\n            result = 0\n            for j,c in enumerate(cost):\n                if i<c:\n                    continue\n                if dp[i-c] == 0 and i!=c:\n                    continue\n                result = max(result,10*dp[i-c]+j+1)\n            dp.append(result)\n        return str(dp[-1])'''\n        cache = {}\n        def helper(remaining):\n            if remaining == 0:\n                return ''\n            if cache.get(remaining) is not None:\n                return cache[remaining]\n            maximum = '0'\n            for i in range(len(cost)):\n                if cost[i] > remaining:\n                    continue\n                result = helper(remaining - cost[i])\n                if result == '0':\n                    continue\n                maximum = larger(maximum, str(i+1) + result)\n            cache[remaining] = maximum\n            return maximum\n\n        def larger(a, b):\n            if len(a) > len(b):\n                return a\n            if len(a) < len(b):\n                return b\n            return max(a, b)\n\n        return helper(target)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'largestNumber'
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: 7597