# A History Lesson

The Pony Express was a mail service operating in the US in 1859-60.





It reduced the time for messages to travel between the Atlantic and Pacific coasts to about 10 days, before it was made obsolete by the transcontinental telegraph.

# How it worked

There were a number of *stations*, where:


* The rider switched to a fresh horse and carried on, or

* The mail bag was handed over to the next rider


# Kata Task


`stations` is a list/array of distances (miles) from one station to the next along the Pony Express route.

Implement the `riders` method/function, to return how many riders are necessary to get the mail from one end to the other.

##  Missing rider

In this version of the Kata a rider may go missing. In practice, this could be for a number of reasons - a lame horse, an accidental fall, foul play... 

After some time, the rider's absence would be noticed at the **next** station, so the next designated rider from there would have to back-track the mail route to look for his missing colleague. The missing rider is then safely escorted back to the station he last came from, and the mail bags are handed to his rescuer (or another substitute rider if necessary). 

`stationX` is the number (2..N) of the station where the rider's absence was noticed.

# Notes

* Each rider travels as far as he can, but never more than 100 miles.

# Example

GIven

* `stations = [43, 23, 40, 13]`

* `stationX = 4`

So

`S1` ...  ... 43 ...  ... `S2` ...  ... 23 ...  ... `S3` ...  ... 40 ...  ... `S4` ...  ... 13 ...  ... `S5`

* Rider 1 gets as far as Station S3
* Rider 2 (at station S3) takes mail bags from Rider 1
* Rider 2 never arrives at station S4
* Rider 3 goes back to find what happened to Rider 2
* Rider 2 and Rider 3 return together back to Station S3
* Rider 3 takes mail bags from Rider 2
* Rider 3 completes the journey to Station S5

**Answer:** 
3 riders




*Good Luck.
DM.*

---

See also
* The Pony Express
* The Pony Express (missing rider)

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def riders(sts, x):\n    st, x, back, n = 0, x-1, 0, 1\n    while True:\n        remain, back = 100 - back, 0\n        while remain >= sts[st]:\n            remain -= sts[st]\n            st += 1\n            if st == x:\n                st -= 1\n                x = -1\n                back = sts[st]\n                break\n            elif st == len(sts):\n                return n\n        n += 1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'riders'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5556