You are given an integer array nums, an integer k, and a $2$D integer array queries where each query is given in the form queries[i] = [index_i, value_i, start_i, x_i].

For each query in order, perform the following actions:

1. Update nums[index_i] to value_i. This modification persists for all subsequent queries.

2. Count the number of subarrays starting at index start_i (that is, contiguous subarrays nums[start_i..j] where start_i $\le j <$ nums.length) such that the product of the elements in the subarray modulo k is equal to x_i.

Return an integer array containing the result for each query.

Constraints:

• $1 \le$ nums[i] $\le 10^9$

• $1 \le$ nums.length $\le 10^5$

• $1 \le$ k $\le 5$

• $1 \le$ queries.length $\le 2 \times 10^4$

• queries[i] == [index_i, value_i, start_i, x_i]

• $0 \le$ index_i $\le$ nums.length $- 1$

• $1 \le$ value_i $\le 10^9$

• $0 \le$ start_i $\le$ nums.length $- 1$

• $0 \le$ x_i $\le$ k $- 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.