<p>A die simulator generates a random number from <code>1</code> to <code>6</code> for each roll. You introduced a constraint to the generator such that it cannot roll the number <code>i</code> more than <code>rollMax[i]</code> (<strong>1-indexed</strong>) consecutive times.</p>

<p>Given an array of integers <code>rollMax</code> and an integer <code>n</code>, return <em>the number of distinct sequences that can be obtained with exact </em><code>n</code><em> rolls</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Two sequences are considered different if at least one element differs from each other.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2, rollMax = [1,1,2,2,2,3]
<strong>Output:</strong> 34
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, rollMax = [1,1,1,1,1,1]
<strong>Output:</strong> 30
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3, rollMax = [1,1,1,2,2,3]
<strong>Output:</strong> 181
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
	<li><code>rollMax.length == 6</code></li>
	<li><code>1 &lt;= rollMax[i] &lt;= 15</code></li>
</ul>

class Solution:
    def dieSimulator(self, n: int, rollMax: List[int]) -> int:
        
        MOD = 10**9 + 7

        @cache
        def itero(idx, val, prev):
            
            if prev > idx:
                return 0
            if idx == 0:
                return 1
            if prev == 0:
                return sum(itero(idx-1, v, p) for v in range(1, 7) for p in range(rollMax[v-1]+1)  if v != val)%MOD
            elif prev == rollMax[val-1]:
                return 0
            else:
                return itero(idx-1, val, prev-1)%MOD
        
        #for val in range(1, 7):
            #for prev in  range(rollMax[val-1]):
                #print(val, prev, itero(n-1, val, prev))

        #print(1, 2, 1, itero(1,2,1))


        return sum(itero(n-1, val, prev) for val in range(1, 7) for prev in range(rollMax[val-1]) )%MOD
107981