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#         def segment_sum(x,k):\n#             # x is worst case, k is number of eggs available\n#             # returns max N for worst case x, eggs k\n#             if k==1:\n#                 return x\n#             return sum(segment_sum(j, k-1)+1 for j in range(x))\n\n#         worst_case=0\n#         while segment_sum(worst_case, K) < N:\n#             worst_case+=1\n#         return worst_case\n\n# class Solution(object):\n#     def superEggDrop(self, K, N):\n#         drops = 0                           # the number of eggs dropped\n#         floors = [0 for _ in range(K + 1)]  # floors[i] is the number of floors that can be checked with i eggs\n\n#         while floors[K] < N:                # until we can reach N floors with K eggs \n\n#             for eggs in range(K, 0, -1):\n#                 floors[eggs] += 1 + floors[eggs - 1]\n#             drops += 1\n\n#         return drops\n\n# class Solution(object):\n#     def superEggDrop(self, K, N):\n#         def f(x):\n#             ans = 0\n#             r = 1\n#             for i in range(1, K+1):\n#                 r *= x-i+1\n#                 r //= i\n#                 ans += r\n#                 if ans >= N: break\n#             return ans\n\n#         lo, hi = 1, N\n#         while lo < hi:\n#             mi = (lo + hi) // 2\n#             if f(mi) < N:\n#                 lo = mi + 1\n#             else:\n#                 hi = mi\n#         return lo\n\nfrom scipy.special import comb, factorial, hyp2f1\nfrom math import log2, floor\n\ndef h(k,n):\n    return round(2**n-1-comb(n,k+1)*hyp2f1(1,k-n+1,k+2,-1))\n\ndef h2(k,n):\n    return sum(comb(n,j) for j in range(1,k+1))\n\ndef fast_sum(k,l):\n    s = 0\n    c = 1\n    for i in range(1,k+1):\n        c *= (l-i+1)/(i)\n        s += c\n    return s\n\ndef e(k, n):\n    if k == 1:\n        return n\n    return sum(e(k-1, j)+1 for j in range(n))\n\ndef f(K, x):\n    ans = 0\n    r = 1\n    for i in range(1, K+1):\n        r *= x-i+1\n        r //= i\n        ans += r\n    return ans\n\nclass Solution:\n    def superEggDrop(self, k: int, n: int) -> int:\n        # best_case = floor(log2(n)+1)\n        # if k >= best_case:\n        #     return best_case\n        if k == 0:\n            return n\n        a, b = 1, n\n        while a < b:\n            c = (a+b)//2\n            if h2(k,c) < n:\n                a = c + 1\n            else:\n                b = c\n        return a'
_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: