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, eggs: int, floors: int) -> int:\n        \n        dp = [[-1 for _ in range(floors+1)] for _ in range(eggs+1)]\n        \n#         int dp(int k, int n) {\n#             if (k <= 0) return 0;\n#             if (k == 1) return n;\n#             if (n <= 1) return n;\n#             if (m_[k][n] != INT_MIN) return m_[k][n];\n\n#             // broken[i]   = dp(k - 1, i - 1) is incresing with i.\n#             // unbroken[i] = dp(k,     n - i) is decresing with i.\n#             // dp[k][n] = 1 + min(max(broken[i], unbroken[i])), 1 <= i <= n\n#             // find the smallest i such that broken[i] >= unbroken[i],\n#             // which minimizes max(broken[i], unbroken[i]).\n#             int l = 1;\n#             int r = n + 1;\n#             while (l < r) {\n#               int m = l + (r - l) / 2;\n#               int broken = dp(k - 1, m - 1);\n#               int unbroken = dp(k, n - m);\n#               if (broken >= unbroken)\n#                 r = m;\n#               else\n#                 l = m + 1;\n#             }\n        \n        def search(eggs, floors):\n            if eggs <= 0:\n                return 0\n            elif eggs == 1:\n                return floors\n            elif floors <= 1:\n                return floors\n            elif dp[eggs][floors] != -1:\n                return dp[eggs][floors]\n            \n            l, r = 1, floors+1\n            while l < r:\n                mid = l + (r-l) // 2\n                broken = search(eggs-1, mid-1)\n                intact = search(eggs, floors-mid)\n                if broken < intact:\n                    l = mid + 1\n                else:\n                    r = mid\n            \n            dp[eggs][floors] = 1 + search(eggs-1, l-1)\n            return dp[eggs][floors]\n        \n        return search(eggs, floors)'
_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: 6364