Subarrays with Sum Divisible by K

Problem Statement

Subarrays with Sum Divisible by K Problem Description A financial institution monitors daily transaction amounts for potential regulatory analysis. Given an array of integers where each element represents the transaction amount for a day, the institution wants to determine the number of continuous time periods (subarrays) for which the total amount is exactly divisible by a given integer K. Your program should compute the count of all such subarrays. The solution must be designed using a divide and conquer approach. Input Variables: N: An integer representing the number of days (1 ≤ N ≤ 10^5). transactions: An array of N integers, where each integer in the range [-10^9, 10^9] represents the transaction amount for that day. K: A positive integer (1 ≤ K ≤ 10^5) which is the divisor used to check for divisibility of the subarray sum. Output: A single integer indicating the total number of contiguous subarrays whose sum is divisible by K. Examples Example 1: Input: N = 5, K = 3, transactio