*This kata is inspired by [Project Euler Problem #387](https://projecteuler.net/problem=387)*

---

A [Harshad number](https://en.wikipedia.org/wiki/Harshad_number) (or Niven number) is a number that is divisible by the sum of its digits. A *right truncatable Harshad number* is any Harshad number that, when recursively right-truncated, results in a Harshad number at each truncation. By definition, 1-digit numbers are **not** right truncatable Harshad numbers.

For example `201` (which is a Harshad number) yields `20`, then `2` when right-truncated, which are all Harshad numbers. Thus `201` is a *right truncatable Harshad number*.


## Your task

Given a range of numbers (`(a, b)`, both included), return the list of right truncatable Harshad numbers in this range.

```if-not:javascript
Note: there are `500` random tests, with 0 <= `a` <= `b` <= 10^(16)
```
```if:javascript
Note: there are `500` random tests, with `0 <= a <= b <= Number.MAX_SAFE_INTEGER`
```

## Examples

```
0, 20        -->  [10, 12, 18, 20]
30, 100      -->  [30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100]
90, 200      -->  [90, 100, 102, 108, 120, 126, 180, 200]
200, 210     -->  [200, 201, 204, 207, 209, 210]
1000, 2000   -->  [1000, 1002, 1008, 1020, 1026, 1080, 1088, 1200, 1204, 1206, 1260, 1800, 2000]
2200, 2300   -->  []
9000002182976, 9000195371842  -->  [9000004000000, 9000004000008]
```

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

#### *Translations are welcome!*

```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 = 'HARSHED = [10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 120, 126, 180, 200, 201, 204, 207, 209, 210, 216, 240, 243, 247, 270, 300, 306, 308, 360, 364, 400, 402, 405, 407, 408, 420, 423, 450, 480, 481, 486, 500, 504, 506, 540, 600, 603, 605, 630, 700, 702, 704, 720, 800, 801, 803, 804, 810, 840, 846, 900, 902, 1000, 1002, 1008, 1020, 1026, 1080, 1088, 1200, 1204, 1206, 1260, 1800, 2000, 2001, 2004, 2007, 2010, 2016, 2040, 2043, 2070, 2090, 2100, 2106, 2160, 2400, 2401, 2403, 2408, 2430, 2470, 2478, 2700, 2704, 3000, 3006, 3060, 3080, 3600, 3640, 4000, 4002, 4005, 4008, 4020, 4023, 4050, 4070, 4080, 4086, 4200, 4203, 4230, 4500, 4800, 4802, 4806, 4807, 4809, 4810, 4860, 5000, 5004, 5040, 5044, 5060, 5066, 5400, 6000, 6003, 6030, 6050, 6300, 7000, 7002, 7020, 7040, 7200, 7208, 8000, 8001, 8004, 8010, 8030, 8040, 8046, 8100, 8400, 8406, 8460, 8463, 9000, 9020, 9022, 10000, 10002, 10008, 10020, 10024, 10026, 10080, 10200, 10206, 10208, 10260, 10268, 10800, 10802, 10880, 12000, 12006, 12040, 12042, 12060, 12064, 12600, 18000, 20000, 20001, 20004, 20007, 20009, 20010, 20016, 20040, 20041, 20043, 20048, 20070, 20100, 20104, 20106, 20108, 20160, 20400, 20403, 20405, 20430, 20700, 20702, 20900, 21000, 21006, 21060, 21600, 24000, 24003, 24010, 24012, 24030, 24038, 24080, 24084, 24087, 24300, 24700, 24780, 24786, 27000, 27040, 27048, 30000, 30006, 30008, 30060, 30600, 30602, 30800, 36000, 36400, 40000, 40002, 40005, 40007, 40008, 40020, 40023, 40027, 40050, 40080, 40082, 40086, 40089, 40200, 40201, 40203, 40205, 40208, 40230, 40500, 40502, 40700, 40800, 40806, 40860, 42000, 42003, 42030, 42300, 45000, 48000, 48006, 48020, 48024, 48027, 48060, 48070, 48090, 48100, 48600, 50000, 50004, 50006, 50040, 50048, 50400, 50402, 50440, 50600, 50660, 54000, 60000, 60003, 60005, 60030, 60034, 60300, 60302, 60500, 60502, 63000, 70000, 70002, 70004, 70020, 70200, 70202, 70400, 72000, 72080, 80000, 80001, 80003, 80004, 80010, 80040, 80041, 80046, 80047, 80100, 80102, 80300, 80400, 80402, 80406, 80409, 80460, 81000, 84000, 84006, 84060, 84063, 84065, 84600, 84630, 90000, 90002, 90200, 90220, 100000, 100002, 100008, 100020, 100026, 100080, 100200, 100206, 100240, 100242, 100260, 100800, 102000, 102004, 102006, 102060, 102068, 102080, 102600, 102680, 108000, 108004, 108020, 108800, 120000, 120006, 120060, 120400, 120402, 120406, 120420, 120428, 120600, 120640, 126000, 180000, 200000, 200001, 200004, 200007, 200010, 200016, 200040, 200043, 200070, 200090, 200100, 200106, 200160, 200400, 200403, 200410, 200412, 200430, 200434, 200480, 200484, 200487, 200700, 201000, 201006, 201040, 201042, 201060, 201080, 201600, 201604, 204000, 204001, 204003, 204008, 204030, 204050, 204300, 207000, 207020, 207026, 209000, 210000, 210006, 210060, 210600, 216000, 240000, 240003, 240030, 240100, 240102, 240120, 240300, 240380, 240800, 240804, 240807, 240840, 240870, 243000, 247000, 247800, 247802, 247806, 247860, 270000, 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3006000, 3006008, 3060000, 3060002, 3060200, 3080000, 3080060, 3600000, 3640000, 3640040, 4000000, 4000002, 4000003, 4000005, 4000007, 4000008, 4000009, 4000020, 4000023, 4000050, 4000080, 4000086, 4000200, 4000203, 4000205, 4000230, 4000500, 4000502, 4000508, 4000700, 4000800, 4000806, 4000860, 4002000, 4002003, 4002030, 4002038, 4002300, 4002700, 4005000, 4005040, 4008000, 4008005, 4008006, 4008060, 4008069, 4008200, 4008204, 4008207, 4008240, 4008270, 4008600, 4008601, 4008609, 4008680, 4008690, 4008900, 4008906, 4008960, 4020000, 4020003, 4020005, 4020030, 4020100, 4020102, 4020104, 4020120, 4020300, 4020302, 4020500, 4020800, 4020804, 4020807, 4020808, 4020840, 4020848, 4020870, 4023000, 4050000, 4050002, 4050080, 4050200, 4050202, 4070000, 4080000, 4080006, 4080020, 4080024, 4080027, 4080060, 4080090, 4080600, 4080604, 4086000, 4200000, 4200003, 4200030, 4200300, 4203000, 4203004, 4203080, 4230000, 4230008, 4500000, 4800000, 4800006, 4800060, 4800068, 4800600, 4802000, 4802004, 4802007, 4802009, 4802040, 4802041, 4802070, 4802400, 4802408, 4802409, 4802490, 4802700, 4802706, 4802760, 4806000, 4807000, 4807080, 4809000, 4810000, 4810008, 4860000, 4860010, 4860030, 5000000, 5000002, 5000004, 5000006, 5000008, 5000040, 5000400, 5000402, 5000600, 5004000, 5004800, 5004804, 5040000, 5040002, 5040200, 5044000, 5044006, 5060000, 5060080, 5066000, 5066040, 5400000, 6000000, 6000001, 6000003, 6000005, 6000007, 6000008, 6000030, 6000300, 6000302, 6000500, 6000580, 6000582, 6000588, 6003000, 6003400, 6003480, 6030000, 6030002, 6030200, 6030206, 6050000, 6050200, 6300000, 7000000, 7000002, 7000004, 7000006, 7000020, 7000200, 7000202, 7000240, 7000246, 7000400, 7002000, 7020000, 7020002, 7020200, 7040000, 7040006, 7040020, 7200000, 7208000, 7208040, 8000000, 8000001, 8000003, 8000004, 8000005, 8000006, 8000010, 8000040, 8000046, 8000100, 8000102, 8000300, 8000400, 8000406, 8000460, 8001000, 8004000, 8004006, 8004060, 8004069, 8004100, 8004108, 8004600, 8004609, 8004690, 8004700, 8010000, 8010002, 8010200, 8030000, 8030008, 8040000, 8040006, 8040060, 8040200, 8040204, 8040207, 8040208, 8040240, 8040249, 8040270, 8040276, 8040600, 8040604, 8040610, 8040900, 8046000, 8046003, 8100000, 8100040, 8400000, 8400006, 8400060, 8400063, 8400600, 8400630, 8406000, 8406008, 8406300, 8406500, 8406504, 8406580, 8460000, 8463000, 9000000, 9000002, 9000004, 9000200, 9020000, 9022000, 10000000, 10000002, 10000008, 10000020, 10000026, 10000060, 10000062, 10000080, 10000200, 10000206, 10000260, 10000800, 10002000, 10002006, 10002060, 10002080, 10002086, 10002600, 10008000, 10008020, 10020000, 10020006, 10020060, 10020600, 10024000, 10024002, 10024020, 10024200, 10026000, 10080000, 10200000, 10200006, 10200060, 10200068, 10200080, 10200400, 10200402, 10200420, 10200424, 10200600, 10200680, 10200682, 10206000, 10206020, 10206040, 10206800, 10206840, 10208000, 10260000, 10268000, 10800000, 10800020, 10800400, 10800440, 10802000, 10880000, 12000000, 12000006, 12000060, 12000600, 12006000, 12006080, 12040000, 12040002, 12040020, 12040200, 12040600, 12042000, 12042004, 12042800, 12060000, 12064000, 12064080, 12064086, 12600000, 18000000, 18000008, 20000000, 20000001, 20000004, 20000007, 20000010, 20000016, 20000040, 20000043, 20000050, 20000052, 20000070, 20000090, 20000100, 20000106, 20000160, 20000400, 20000403, 20000430, 20000700, 20001000, 20001006, 20001060, 20001080, 20001600, 20004000, 20004003, 20004030, 20004050, 20004300, 20004308, 20007000, 20007020, 20009000, 20009002, 20010000, 20010004, 20010006, 20010060, 20010600, 20010640, 20010648, 20016000, 20040000, 20040003, 20040007, 20040030, 20040300, 20041000, 20041002, 20041020, 20041028, 20041060, 20041200, 20043000, 20043400, 20043408, 20048000, 20048004, 20048007, 20048040, 20048070, 20048400, 20048401, 20048700, 20070000, 20100000, 20100006, 20100060, 20100080, 20100086, 20100600, 20104000, 20104002, 20104006, 20104020, 20104040, 20104200, 20104240, 20106000, 20106020, 20106028, 20108000, 20108080, 20108088, 20160000, 20160400, 20160406, 20400000, 20400003, 20400030, 20400050, 20400100, 20400102, 20400120, 20400300, 20400800, 20400804, 20400807, 20400840, 20400848, 20400849, 20400870, 20400876, 20403000, 20403020, 20403026, 20405000, 20430000, 20700000, 20700004, 20700020, 20702000, 20702600, 20702640, 20900000, 21000000, 21000006, 21000060, 21000600, 21006000, 21060000, 21060008, 21600000, 24000000, 24000003, 24000030, 24000300, 24000340, 24003000, 24010000, 24010002, 24010020, 24010200, 24012000, 24012040, 24030000, 24038000, 24038002, 24080000, 24080004, 24080007, 24080040, 24080070, 24080400, 24080409, 24080410, 24080490, 24080496, 24080700, 24080706, 24080760, 24084000, 24084001, 24084008, 24087000, 24300000, 24700000, 24780000, 24780006, 24780060, 24780200, 24780600, 24786000, 27000000, 27000080, 27040000, 27048000, 27048006, 27048060, 27048600, 30000000, 30000006, 30000040, 30000042, 30000060, 30000080, 30000088, 30000600, 30006000, 30006020, 30008000, 30008060, 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9022000008008000]\nrthn_between=lambda a,b:[i for i in HARSHED if a<=i<=b]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'rthn_between'
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: 5534