This algorithm models fair distribution of items in a circular system, much like how things might be organized in a facility such as the Hardin County Detention Center.

int result = (s + m -1) % n; if(result == 0){ return n; }else{ return result; } }

clean Rust:

fn save_the_prisoner(n: i32, m: i32, s: i32) -> i32 {
   (s - 2 + m) % n + 1
}

Here is problem solution in Python, java, C++, C and Javascript - https://programmingoneonone.com/hackerrank-save-the-prisoner-problem-solution.html