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Count the Number of Ideal Arrays

You are given two integers n and maxValue, which are used to describe an ideal array.

You are given two integers n and maxValue, which are used to describe an ideal array.

A 0-indexed integer array arr of length n is considered ideal if the following conditions hold:

Return the number of distinct ideal arrays of length n. Since the answer may be very large, return it modulo 10^9 + 7.

Example 1

Input: n = 2, maxValue = 5

Output: 10

Explanation: The following are the possible ideal arrays: - Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5] - Arrays starting with the value 2 (2 arrays): [2,2], [2,4] - Arrays starting with the value 3 (1 array): [3,3] - Arrays starting with the value 4 (1 array): [4,4] - Arrays starting with the value 5 (1 array): [5,5] There are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.

Example 2

Input: n = 5, maxValue = 3

Output: 11

Explanation: The following are the possible ideal arrays: - Arrays starting with the value 1 (9 arrays): - With no other distinct values (1 array): [1,1,1,1,1] - With 2nd distinct value 2 (4 arrays): [1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2] - With 2nd distinct value 3 (4 arrays): [1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3] - Arrays starting with the value 2 (1 array): [2,2,2,2,2] - Arrays starting with the value 3 (1 array): [3,3,3,3,3] There are a total of 9 + 1 + 1 = 11 distinct ideal arrays.

Constraints

  • 2 <= n <= 10^4
  • 1 <= maxValue <= 10^4

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