1223.

Dice Roll Simulation

Hard

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