I always thought that my old friend John was rather richer than he looked, but I never knew exactly how much money he actually had. One day (as I was plying him with questions) he said:

* "Imagine I have between `m` and `n` Zloty..." (or did he say Quetzal? I can't remember!)
* "If I were to buy **9** cars costing `c` each, I'd only have 1 Zloty (or was it Meticals?) left."
* "And if I were to buy **7** boats at `b` each, I'd only have 2 Ringglets (or was it Zloty?) left."

Could you tell me in each possible case:

1. how much money `f` he could possibly have ?
2. the cost `c` of a car?
3. the cost `b` of a boat?

So, I will have a better idea about his fortune. Note that if `m-n` is big enough, you might have a lot of possible answers. 

Each answer should be given as `["M: f", "B: b", "C: c"]` and all the answers as `[ ["M: f", "B: b", "C: c"], ... ]`. "M" stands for money, "B" for boats, "C" for cars.

**Note:** `m, n, f, b, c` are positive integers, where `0 <= m <= n` or `m >= n >= 0`. `m` and `n` are inclusive.


## Examples:
```
howmuch(1, 100)      => [["M: 37", "B: 5", "C: 4"], ["M: 100", "B: 14", "C: 11"]]
howmuch(1000, 1100)  => [["M: 1045", "B: 149", "C: 116"]]
howmuch(10000, 9950) => [["M: 9991", "B: 1427", "C: 1110"]]
howmuch(0, 200)      => [["M: 37", "B: 5", "C: 4"], ["M: 100", "B: 14", "C: 11"], ["M: 163", "B: 23", "C: 18"]]
```

Explanation of the results for `howmuch(1, 100)`:

* In the first answer his possible fortune is **37**:
 * so he can buy 7 boats each worth 5: `37 - 7 * 5 = 2`
 * or he can buy 9 cars worth 4 each: `37 - 9 * 4 = 1`
* The second possible answer is **100**:
 * he can buy 7 boats each worth 14: `100 - 7 * 14 = 2`
 * or he can buy 9 cars worth 11: `100 - 9 * 11 = 1`

# Note
See "Sample Tests" to know the format of the return.

```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 = 'from math import ceil\n\n# All the solutions I saw were so slow, iterating the whole m -> n\n# For M, the solutions are the 37 + 63k in [m, n]\n# You can find that with chinese remainder theorem, or just by looking at the examples\n# Then just calculate B and C for each\n# No need to waste time doing useless loops\ndef howmuch(m, n):\n    m, n = min(m, n), max(m, n)\n    x = max(0, ceil((m-37)/63))\n    return [[f"M: {y}", f"B: {(y-2)//7}", f"C: {(y-1)//9}"] for y in range(37 + 63*x, n+1, 63)]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'howmuch'
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: 6185