Daily Challenge #96 - Easter Egg Crush Test

Eulampy has a collection of some almost identical Fabergè eggs. One day his friend Tempter said to him:

• Do you see that skyscraper? And can you tell me a maximal floor that if you drop your egg from will not crack it?
• No, - said Eulampy.
• But if you give me N eggs, - says Tempter - I'll tell you an answer.
• Deal - said Eulampy. But I have one requirement before we start this: if I will see more than M falls of egg, my heart will be crushed instead of egg. So you have only M tries to throw eggs. Would you tell me an exact floor with this limitation?

Your task is to help Tempter - write a function

height :: Integer -> Integer -> Integer
height n m = -- see text

that takes 2 arguments - the number of eggs n and the number of trys m - you should calculate maximum skyscraper height (in floors), in which it is guaranteed to find an exactly maximal floor from which that an egg won't crack it.

Which means,

• You can throw an egg from a specific floor every try

• Every egg has the same, certain durability - if they're thrown from a certain floor or below, they won't crack. Otherwise, they crack.

• You have n eggs and m tries

What is the maximum height, such that you can always determine which floor the target floor is when the target floor can be any floor between 1 to this maximum height?

Examples
height 0 14 = 0
height 2 0 = 0
height 2 14 = 105
height 7 20 = 137979

Data range
n <= 20000
m <= 20000

This challenge comes from Ivana on CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

Want to propose a challenge idea for a future post? Email yo+challenge@dev.to with your suggestions!