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 = '\nfrom math import inf\nfrom typing import List\n\nclass Solution:\n\n    def superEggDrop(self, K: int, N: int) -> int:\n        self.memo = {}\n        return self.rec(K, N)\n\n\n    def rec(self, i, j):\n        if i == 1:\n            return j\n        if j == 0 or j == 1:\n            return j\n        if (i, j) in self.memo:\n            return self.memo[i, j]\n        lo, hi = 0, j\n        while lo < hi:\n            mid = lo + (hi - lo) // 2\n            left, right = self.rec(i - 1, mid - 1), self.rec( i, j - mid)\n            if left < right:\n                lo = mid + 1\n            else:\n                hi = mid\n        res = 1 + self.max(self.rec(i - 1, lo - 1), self.rec(i, j - lo))\n        self.memo[i, j] = res\n        return res \n        \n\n    def dp(self, K: int, N: int) -> int:\n        #dp[i][j] - i eggs for j floors\n        dp = [[inf for _ in range(N + 1)] for _ in range(K + 1)]\n        #dp[i][0] -> 0, dp[1][j] -> j, dp[i][1] -> 1\n        for i in range(K + 1):\n            dp[i][0] = 0\n            dp[i][1] = 1\n        for j in range(N + 1):\n            dp[1][j] = j\n\n        for i in range(2, K + 1):\n            for j in range(2, N + 1):\n                left, right = 0, j\n                while left < right:\n                    mid = left + (right - left) // 2\n                    if dp[i - 1][mid - 1] < dp[i][j - mid]:\n                        left = mid + 1\n                    else:\n                        right = mid \n                dp[i][j] = 1 + self.max(dp[i - 1][left - 1], dp[i][j - left])\n                #for k in range(i, j + 1):\n                #    dp[i][j] = self.min(dp[i][j] , 1 + self.max(dp[i - 1][k - 1], dp[i][j - k])\n        \n        return dp[K][N] \n\n    def min(self, a, b):\n        return a if a < b else b\n    def max(self, a, b):\n        return a if a > b else b\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: 5846