2261 - K Divisible Elements Subarrays\.

Medium

Given an integer array nums and two integers k and p, return the number of distinct subarrays which have at most k elements divisible by p.

Two arrays nums1 and nums2 are said to be distinct if:

• They are of different lengths, or

• There exists at least one index i where nums1[i] != nums2[i].

A subarray is defined as a non-empty contiguous sequence of elements in an array.

Example 1:

Input: nums = **2** ,3,3, **2** , **2** , k = 2, p = 2

Output: 11

Explanation:

The elements at indices 0, 3, and 4 are divisible by p = 2.

The 11 distinct subarrays which have at most k = 2 elements divisible by 2 are:

2, 2,3, 2,3,3, 2,3,3,2, 3, 3,3, 3,3,2, 3,3,2,2, 3,2, 3,2,2, and 2,2.

Note that the subarrays 2 and 3 occur more than once in nums, but they should each be counted only once.

The subarray 2,3,3,2,2 should not be counted because it has 3 elements that are divisible by 2.

Example 2:

Input: nums = 1,2,3,4, k = 4, p = 1

Output: 10

Explanation:

All element of nums are divisible by p = 1.

Also, every subarray of nums will have at most 4 elements that are divisible by 1.

Since all subarrays are distinct, the total number of subarrays satisfying all the constraints is 10.

Constraints:

• 1 <= nums.length <= 200

• 1 <= nums[i], p <= 200

• 1 <= k <= nums.length