Given an array A of N integers and an integer K, write a program to print the number of subarrays in A whose sum is divisible by K.

Sure, here is a step-by-step approach to solve the problem:

1. Initialize a variable count to 0, which will keep track of the number of subarrays whose sum is divisible by K.

2. Create a dictionary remainder_count to store the count of remainders obtained when the cumulative sum of elements in the array is divided by K. Initialize remainder_count with a single key-value pair: (0, 1), as the cumulative sum of an empty subarray is 0.

3. Initialize a variable cumulative_sum to 0, which will store the cumulative sum of elements in the array.

4. Iterate through each element num in the array A.

5. Update the cumulative_sum by adding num to it.

6. Calculate the remainder remainder when cumulative_sum is divided by K.

7. If remainder is negative, add K to it to make it positive. This is done to handle negative remainders.

8. If remainder exists in remainder_count, increment count by the value associated with remainder in remainder_count.

9. If remainder does not exist in remainder_count, add it to remainder_count with a value of 1.

10. Increment the value associated with remainder in remainder_count by 1.

11. After iterating through all the elements in the array, print the value of count, which represents the number of subarrays whose sum is divisible by K.

Here is a sample implementation in Python:

def count_subarrays(A, K):
    count = 0
    remainder_count = {0: 1}
    cumulative_sum = 0

    for num in A:
        cumulative_sum += num
        remainder = cumulative_sum % K

        if remainder < 0:
            remainder += K

        if remainder in remainder_count:
            count += remainder_count[remainder]

        remainder_count[remainder] = remainder_count.get(remainder, 0) + 1

    return count

# Example usage
A = [4, 5, 0, -2, -3, 1]
K = 5
result = count_subarrays(A, K)
print(result)  # Output: 7

This implementation has a time complexity of O(N), where N is the length of the array A.