{ "data": { "question": { "questionId": "1343", "questionFrontendId": "1223", "boundTopicId": null, "title": "Dice Roll Simulation", "titleSlug": "dice-roll-simulation", "content": "

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.

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Given an array of integers rollMax and an integer n, return the number of distinct sequences that can be obtained with exact n rolls. Since the answer may be too large, return it modulo 109 + 7.

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Two sequences are considered different if at least one element differs from each other.

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Example 1:

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\nInput: n = 2, rollMax = [1,1,2,2,2,3]\nOutput: 34\nExplanation: 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.\n
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Example 2:

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\nInput: n = 2, rollMax = [1,1,1,1,1,1]\nOutput: 30\n
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Example 3:

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\nInput: n = 3, rollMax = [1,1,1,2,2,3]\nOutput: 181\n
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Constraints:

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