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 superEggDrop1(self, K: int, N: int) -> int: # 超时！！！\n        memo = [[2**31-1] * (N+1) for _ in range(K+1)]\n        \n        def dp(k, n):\n            if k == 0: return 0\n            if k == 1: return n\n            if n <= 1: return n\n            \n            if memo[k][n] < 2**31-1:\n                return memo[k][n]\n            \n            ans = memo[k][n]\n            for i in range(1, n+1):\n                ans = min(ans, 1+max(dp(k-1, i-1), dp(k, n-i)))\n                # 极小极大过程！！！alike\n            memo[k][n] = ans\n            return ans\n        return dp(K, N)\n    \n    # D(K-1, i-1), monotonically increasing with i\n    # D(K, N-i) is monotonically decreasing with i!\n    \n    # binary search!\n    # D(K, N) = 1 + min(max(D(K-1, i-1), D(K, N-i))), 1<=i<=N\n    # f(i) = D(K-1, i-1), f(i) is monotonically increasing with i\n    # g(i) = D(K, N-i), g(i) is monotonically decreasing with i\n    \n    # we can use binary search to find i that minimizes max(f(i), g(i))\n    #\n    # 一个函数单调增；一个函数单调减\n    # min (max (f, g))\n    # 就可以使用binary search\n    # f(i) < g(i) 的时候，说明i太小了，需要增大i\n    # f(i) > g(i) 的时候，说明i太大了，需要减少i\n    # 我们需要的是first i, such that f(i) >= g(i)\n    # time complexity = O(KNlogN) smaller than O(K*N*N)\n    # space is same O(KN)\n    \n    def superEggDrop3(self, K: int, N: int) -> int: # 使用binary search，可以得到最好的结果了！\n        memo = [[2**31-1] * (N+1) for _ in range(K+1)]\n        \n        def dp(k, n):\n            if k == 0: return 0\n            if k == 1: return n\n            if n <= 1: return n\n            \n            if memo[k][n] < 2**31-1:\n                return memo[k][n]\n            \n            #ans = memo[k][n]\n            #for i in range(1, n+1):\n            #    ans = min(ans, 1+max(dp(k-1, i-1), dp(k, n-i)))\n                # 极小极大过程！！！alike\n            left = 1\n            right = n + 1\n            res = 2**31-1\n            while left < right:\n                mid = left + (right - left) // 2\n                broken = dp(k-1, mid-1)\n                notbroken = dp(k, n-mid)\n                if broken >= notbroken: # f(mid) >= g(mid) 最小的mid!\n                    right = mid\n                    res = min(res, broken+1)\n                else:\n                    left = mid + 1\n                    res = min(res, notbroken+1)\n            \n            memo[k][n] = res #1 + max(dp(k-1, left-1), dp(k, n-left))\n            return memo[k][n]\n        return dp(K, N)\n    \n    def superEggDrop(self, K, N):\n        amax = 2**31-1\n        memo = [[amax] * (N+1) for _ in range(K+1)]\n        \n        def dp(k, n):\n            if k == 0: return 0\n            if k == 1: return n\n            if n <= 1: return n # this time k>1\n            \n            if memo[k][n] != amax:\n                return memo[k][n]\n            left = 1\n            right = n + 1\n            while left < right:\n                mid = left + (right - left)//2\n                broken = dp(k-1, mid-1)\n                notbroken = dp(k, n-mid) # mid+1 to N\n                if broken >= notbroken:\n                    right = mid\n                else:\n                    left = mid + 1\n            ans = 1 + max(dp(k-1, left-1), dp(k, n-left))\n            memo[k][n] = ans\n            return ans\n        return dp(K, N)\n    \n    def superEggDrop2(self, K: int, N: int) -> int: # 使用binary search，很好了！\n        memo = [[2**31-1] * (N+1) for _ in range(K+1)]\n        \n        def dp(k, n):\n            if k == 0: return 0\n            if k == 1: return n\n            if n <= 1: return n\n            \n            if memo[k][n] < 2**31-1:\n                return memo[k][n]\n            \n            #ans = memo[k][n]\n            #for i in range(1, n+1):\n            #    ans = min(ans, 1+max(dp(k-1, i-1), dp(k, n-i)))\n                # 极小极大过程！！！alike\n            left = 1\n            right = n + 1\n            while left < right:\n                mid = left + (right - left) // 2\n                # broken >= not_broken\n                if dp(k-1, mid-1) >= dp(k, n-mid): # f(mid) >= g(mid) 最小的mid!\n                    right = mid\n                else:\n                    left = mid + 1\n            # 通过binary search找到left是核心！找极值点！\n            memo[k][n] = 1 + max(dp(k-1, left-1), dp(k, n-left))\n            return memo[k][n]\n        return dp(K, N)\n    \n    def superEggDrop4(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        # 还是使用了binary search! 速度很快啊！！！\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'
_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: 6440