With your birthday coming up soon, your eccentric friend sent you a message to say "happy birthday":

    hhhappyyyy biirrrrrthddaaaayyyyyyy to youuuu
    hhapppyyyy biirtttthdaaay too youuu
    happy birrrthdayy to youuu
    happpyyyy birrtthdaaay tooooo youu

At first it looks like a song, but upon closer investigation, you realize that your friend hid the phrase "happy birthday" thousands of times inside his message. In fact, it contains it more than 2 million times! To thank him, you'd like to reply with exactly how many times it occurs.

To count all the occurences, the procedure is as follows: look through the paragraph and find a `'h'`; then find an `'a'` later in the paragraph; then find an `'p'` after that, and so on. Now count the number of ways in which you can choose letters in this way to make the full phrase.

More precisely, given a text string, you are to determine how many times the search string appears as a sub-sequence of that string.

Write a function called `countSubsequences` that takes two arguments: `needle`, the string to be search for and `haystack`, the string to search in. In our example, `"happy birthday"` is the needle and the birthday message is the haystack. The function should return the number of times `needle` occurs as a sub-sequence of `haystack`.  Spaces are also considered part of the needle.

Since the answers can be very large, return only the last 8 digits of the answer in case it exceeds 8 digits. The answers to the test cases will all be shorter than 8 digits.

```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 functools import lru_cache\n\ndef count_subsequences(a, b):\n    n, m = len(a), len(b)\n    \n    @lru_cache(maxsize=None)\n    def f(i, j):\n        if j < i: return 0\n        if i == 0: return 1\n        return f(i, j - 1) + (f(i - 1, j - 1) if a[i - 1] == b[j - 1] else 0)\n        \n    return f(n, m) % 100_000_000'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'count_subsequences'
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: 23254