You are given K eggs, and you have access to a building with N floors from 1 to N. 
Each egg is identical in function, and if an egg breaks, you cannot drop it again.
You know that there exists a floor F with 0 <= F <= N such that any egg dropped at a floor higher than F will break, and any egg dropped at or below floor F will not break.
Each move, you may take an egg (if you have an unbroken one) and drop it from any floor X (with 1 <= X <= N). 
Your goal is to know with certainty what the value of F is.
What is the minimum number of moves that you need to know with certainty what F is, regardless of the initial value of F?
 



Example 1:
Input: K = 1, N = 2
Output: 2
Explanation: 
Drop the egg from floor 1.  If it breaks, we know with certainty that F = 0.
Otherwise, drop the egg from floor 2.  If it breaks, we know with certainty that F = 1.
If it didn't break, then we know with certainty F = 2.
Hence, we needed 2 moves in the worst case to know what F is with certainty.


Example 2:
Input: K = 2, N = 6
Output: 3


Example 3:
Input: K = 3, N = 14
Output: 4

 
Note:

1 <= K <= 100
1 <= N <= 10000

```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 = 'class Solution:\n    def superEggDrop(self, K: int, N: int) -> int:\n        dict_soln = {}\n        return self.dp(K, N, dict_soln)\n    def dp(self, k, n, dict_soln):\n        if n == 0:\n            return 0\n        if k == 0:\n            return -1\n        if k == 1:\n            return n\n        if (k, n) in dict_soln:\n            return dict_soln[(k, n)]\n        # test at x (x = 1, ..., n)\n        # dp(k, n) = min_{x = 1, ..., n} max(dp(k, n - x), dp(k - 1, x - 1)) + 1\n        left = 1\n        right = n\n        while True:\n            if left - right == -1:\n                tmp1 = self.dp(k - 1, left - 1, dict_soln)\n                tmp2 = self.dp(k, n - left, dict_soln)\n                tmp3 = self.dp(k - 1, right - 1, dict_soln)\n                tmp4 = self.dp(k, n - right, dict_soln)\n                tmpl = max(tmp1, tmp2)\n                tmpr = max(tmp3, tmp4)\n                if tmpl < tmpr:\n                    dict_soln[(k, n)] = tmpl + 1\n                    return dict_soln[(k, n)]\n                else:\n                    dict_soln[(k, n)] = tmpr + 1\n                    return dict_soln[(k, n)]\n            xmid = (left + right) // 2\n            tmp1 = self.dp(k - 1, xmid - 1, dict_soln)\n            tmp2 = self.dp(k, n - xmid, dict_soln)\n            if tmp1 > tmp2:\n                right = xmid\n            elif tmp1 < tmp2:\n                left = xmid\n            else:\n                dict_soln[(k, n)] = tmp1 + 1\n                return dict_soln[(k, n)]\n            \n    \n        \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'superEggDrop'
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: 6068