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887. Super Egg Drop


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
    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



    1. 1 <= K <= 100
    2. 1 <= N <= 10000

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