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        # dynamic programming\n        # dp[i][j][k] # at pos i, we end with j, and the number of continuous of j at the end is k\n\n        dp = [ [ [ 0 for k in range(rollMax[j] + 1)] for j in range(6)] for _ in range(n)]\n        \n        for j in range(6):\n            dp[0][j][1] = 1\n        \n        for i in range(n):\n            for j in range(6):\n                for k in range(2, rollMax[j] + 1): # 这里 原则上来说应该写成 range(2)开始，因为 k-1>=1,但是写成 1也没有关系，因为 k-1=0, += 0, 没有影响。\n                    dp[i][j][k] += dp[i - 1][j][k - 1]\n                \n                for otherj in range(6):\n                    if otherj != j:\n                        for k in range(1, rollMax[otherj] + 1):\n                            dp[i][j][1] += dp[i - 1][otherj][k]\n        # print(\\"dp=\\", dp)\n        return sum([sum(x)%(10**9 + 7) for x in dp[-1]])%(10**9 + 7)\n# 题解，这种计算个数的一般都是动态规划。注意到题目中 rollMax[i] >=1说明 只要上一个不一样，那么我这次出那个数字都是可以的。最后别忘了求 mod\n# 动态规划， 最重要的是，要记录哪种状态。这里 要求的是 某个 number 不能连续超过 rollMax[j]次，那么显然我们需要记录这件事。然后当前的位置需要记录，最后一个数字是什么需要记录，最后一个数字出现多少次，需要记录，于是三维 dp 出现了。\n\n#dp[i][j][k] 代表 到第 i 个位置时，以数字 j 结尾，结尾处 连续出现 k 次。 那么其实这里就要求 k >= 1 的，因为以 j结尾了，那么肯定至少有一个数字了。\n# dp 三维数组的维度怎么确定呢？ i，j 是很显然，一个是 n，一个是6，那么k维度，我们用 roolMax[j] + 1 这个维度，因为 我们出现的个数 0，1，2，3，4，。。。，一直到 roolMax[j] 都是可以的，所以 range （roolMax[j] + 1).\n# 那么 j 用 range(6) = 0, 1, 2, 3, 4,5 这里是没有关系的，正好和 roolMax[j] 的 index 对应起来。 不用 换成 1，2，3，4，5，6.\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: 8134