A die simulator generates a random number from 1 to 6 for each roll. You introduced a constraint to the generator such that it cannot roll the number i more than rollMax[i] (1-indexed) consecutive times. 
Given an array of integers rollMax and an integer n, return the number of distinct sequences that can be obtained with exact n rolls.
Two sequences are considered different if at least one element differs from each other. Since the answer may be too large, return it modulo 10^9 + 7.
 
Example 1:
Input: n = 2, rollMax = [1,1,2,2,2,3]
Output: 34
Explanation: There will be 2 rolls of die, if there are no constraints on the die, there are 6 * 6 = 36 possible combinations. In this case, looking at rollMax array, the numbers 1 and 2 appear at most once consecutively, therefore sequences (1,1) and (2,2) cannot occur, so the final answer is 36-2 = 34.

Example 2:
Input: n = 2, rollMax = [1,1,1,1,1,1]
Output: 30

Example 3:
Input: n = 3, rollMax = [1,1,1,2,2,3]
Output: 181

 
Constraints:

1 <= n <= 5000
rollMax.length == 6
1 <= rollMax[i] <= 15

```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 dieSimulator(self, n: int, rollMax: List[int]) -> int:\n        \n        faces = len(rollMax)\n        # [n + 1][faces + 1] dimensional dp array\n        dp = [[0 for i in range(faces + 1)] for j in range(n + 1)]\n        \n        # initialization\n        # roll 0 times, the total combination is 1\n        dp[0][faces] = 1\n        # roll 1 times, the combinations that end at face j is 1\n        for j in range(faces):\n            dp[1][j] = 1\n        # roll 1 times, the total combination is faces = 6\n        dp[1][faces] = faces\n        \n        # then roll dices from 2 times, until n times\n        for i in range(2, n + 1):\n            # iterate through each column (face)\n            for j in range(faces):\n                # at each [i, j], trying to go up (decrease i) and collect all the sum of previous state\n                k = 1\n                while i >= k and k <= rollMax[j]:\n                    dp[i][j] += dp[i - k][faces] - dp[i - k][j]\n                    k+=1\n            # update total sum of this row\n            dp[i][faces] = sum(dp[i])\n        \n        return dp[n][faces] % 1000000007\n        \n        \n                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'dieSimulator'
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: 6636