💡 Beginner-Friendly Guide 'Minimum Operations to Equalize Binary String' - Problem 3666 (C++, Python, JavaScript)

In this challenge, we tackle a puzzle that feels like a digital light switch game. We need to find the most efficient way to turn all zeros into ones, but there is a catch: every move requires us to flip exactly $k$ switches at once. Problem Summary You're given: A binary string $s$ consisting of '0's and '1's. An integer $k$, representing the exact number of indices you must flip in a single operation. Your goal: Find the minimum number of operations required to make the entire string consist of only '1's. If it is impossible to reach this state, return -1. Intuition To solve this efficiently, we don't need to simulate every possible flip. Instead, we can use a mathematical approach based on the total number of zeros. Every time we flip an index, we either change a '0' to a '1' (reducing the zero count by 1) or a '1' to a '0' (increasing the zero count by 1). If we perform $i$ operations, we have made a total of $i \times k$ flips. Let $z$ be the initial number of zeros. After $i$ ope