Problem Statement

Subarrays with Sum Divisible by K Problem Description An analytics team reviews a ledger of daily transaction amounts for compliance purposes. Given an array where each entry is the transaction total for one day, they want to know how many continuous stretches of days (subarrays) have a combined total that divides evenly by a given integer K. Your program must count all such subarrays, and it must solve the problem 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, transactions = [1, 2, 3, 4, 1] Output: 4 Explanation: The continuous subarra