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 itagain.
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 (with1 <= X <= N).
Your goal is to knowwith certaintywhat the value of F is.
What is the minimum number of moves that you need to know with certaintywhat 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
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