2338 - Count the Number of Ideal Arrays.

Hard

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:

• Every arr[i] is a value from 1 to maxValue, for 0 <= i < n.

• Every arr[i] is divisible by arr[i - 1], for 0 < i < n.

Return the number of distinct ideal arrays of length n. Since the answer may be very large, return it modulo <code>10⁹ + 7</code>.

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):

• 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:

• <code>2 <= n <= 10⁴</code>

• <code>1 <= maxValue <= 10⁴</code>