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    # Basic solution: 3 dimensions, n rolls, last roll, last consecutive count -> O(n^2)\n    # Can we reduce to O(n) or O(nlogn)? Seems not.\n    d = {}\n    def dp(n, v, k): # n rolls, last is v, v has at most k consecutive (k > 1. Notice: don't handle k == 0, since it will include others repeated, e.g. k == 0 for 1 includes k == 0 for 2, etc.)\n#       if n == 1:\n#         return 1 if k == 1 else 0\n#       if (n, v, k) not in d:\n#         if k == 1:\n#           d[(n, v, k)] = 0\n#           for i, lim in enumerate(rollMax):\n#             if i != v:\n#               d[(n, v, k)]\n#         else:\n#           d[(n, v, k)] = dp(n-1, v, k-1)\n      \n      if n == 1:\n        return 1\n      if (n, v, k) not in d:\n        if k == 1:\n          d[(n, v, k)] = 0\n          for i, lim in enumerate(rollMax):\n            if i != v:\n              d[(n, v, k)] += dp(n-1, i, lim) # All others\n        elif k == 2:\n          d[(n, v, k)] = dp(n, v, 1) + dp(n-1, v, k-1)\n        else:\n          # atmost(n, v, k) = atmost(n, v, k-1) + exactly(n, v, k) = atmost(n, v, k-1) + exactly(n-1, v, k-1) = atmost(n, v, k-1) + atmost(n-1, v, k-1) - atmost(n-1, v, k-2)\n          d[(n, v, k)] = dp(n, v, k-1) + dp(n-1, v, k-1) - dp(n-1, v, k-2)\n      return d[(n, v, k)]\n    \n    def get_exact(n, v, k):\n      if k == 1:\n        return dp(n, v, k)\n      return dp(n, v, k) - dp(n, v, k-1)\n    \n    res = 0\n    for i, lim in enumerate(rollMax):\n      for j in range(1, lim+1):\n        res += get_exact(n, i, j)\n\n    return res % (10**9 + 7)"
_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: 8320