A happy string is a string that:

consists only of letters of the set ['a', 'b', 'c'].
s[i] != s[i + 1] for all values of i from 1 to s.length - 1 (string is 1-indexed).

For example, strings "abc", "ac", "b" and "abcbabcbcb" are all happy strings and strings "aa", "baa" and "ababbc" are not happy strings.
Given two integers n and k, consider a list of all happy strings of length n sorted in lexicographical order.
Return the kth string of this list or return an empty string if there are less than k happy strings of length n.
 
Example 1:
Input: n = 1, k = 3
Output: "c"
Explanation: The list ["a", "b", "c"] contains all happy strings of length 1. The third string is "c".

Example 2:
Input: n = 1, k = 4
Output: ""
Explanation: There are only 3 happy strings of length 1.

Example 3:
Input: n = 3, k = 9
Output: "cab"
Explanation: There are 12 different happy string of length 3 ["aba", "abc", "aca", "acb", "bab", "bac", "bca", "bcb", "cab", "cac", "cba", "cbc"]. You will find the 9th string = "cab"

Example 4:
Input: n = 2, k = 7
Output: ""

Example 5:
Input: n = 10, k = 100
Output: "abacbabacb"

 
Constraints:

1 <= n <= 10
1 <= k <= 100

```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 = "import math\n\nclass Solution:\n    def __init__(self):\n        self.happy_string = ''\n    \n    def getHappyString(self, n: int, k: int) -> str:\n        # determine starting character\n        poss_per_group = 2 ** (n - 1)\n        group_num = math.ceil(k / poss_per_group) - 1\n        starting_char = ''\n        \n        # check to make sure there are at least k happy strings\n        if k > poss_per_group * 3:\n            return ''\n        \n        if group_num == 0:\n            self.happy_string += 'a'\n        elif group_num == 1:\n            self.happy_string += 'b'\n        else:\n            self.happy_string += 'c'\n            \n        self.findNextChar(group_num, n - 1, group_num * poss_per_group, (group_num + 1) * poss_per_group, k)\n        return self.happy_string\n        \n    def findNextChar(self, char_index: int, n: int, start: int, end: int, k: int) -> None:\n        if n != 0:\n            lower_index = -1\n            upper_index = -1\n            \n            # 0 = 'a', 1 = 'b', 2 = 'c'\n            if char_index == 0:\n                lower_index = 1\n                upper_index = 2\n            elif char_index == 1:\n                lower_index = 0\n                upper_index = 2\n            else:\n                lower_index = 0\n                upper_index = 1\n                \n            midpoint = int((start + end ) / 2)\n            if (k <= midpoint):\n                self.happy_string += self.indexToStr(lower_index)\n                self.findNextChar(lower_index, n - 1, start, midpoint, k)\n            else:\n                self.happy_string += self.indexToStr(upper_index)\n                self.findNextChar(upper_index, n - 1, midpoint, end, k)                \n                \n    def indexToStr(self, index: int) -> str:\n        if index == 0:\n            return 'a'\n        elif index == 1:\n            return 'b'\n        else:\n            return 'c'\n                \n            \n            \n        \n            \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'getHappyString'
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: 5984