IP Address Transformation / Increment-with-carry Variant ("One Step Dance" variant)

Problem: IPv4 String Transformation Variant (with carry + range constraint) You are given IPv4 address strings in the form "a.b.c.d", where each segment is a decimal integer. Define an operation similar to an “increment with carry” on IPv4: Treat the IPv4 as 4 base-256 digits (each in [0,255]). Increment the lowest segment by 1. If a segment becomes 256, set it to 0 and carry 1 to the next higher segment (e.g., 0.0.0.255 -> 0.0.1.0). In addition, you are given a numeric range [start, end] (both IPv4 strings). During the process, you may only generate/visit IPs that lie within the inclusive range [start, end], where comparison is by IPv4 numeric value (i.e., interpret a.b.c.d as a 32-bit integer). Tasks: Parse IPv4 strings to numeric form and convert back to string form. Implement the above increment-with-carry under the range constraint. (If required) Compute the minimum number of operations to reach end starting from start; return -1 if impossible. Input start: IPv4 string end: IPv4 string Output An integer: minimum number of operations (or -1 if unreachable) Example Input: start = "0.0.0.255", end = "0.0.1.0" Output: 1 Input: start = "0.0.0.1", end = "0.0.0.0" Output: -1 Example Input 0.0.0.255 0.0.1.0 Output 1