Egg Drop

A building has floors numbered 1 to floors, and you have eggs identical eggs. Somewhere there is a safe height s, from 0 to floors: an egg dropped from floor s or lower survives, and an egg dropped from any floor above s breaks. A broken egg is gone for good; an egg that survives can be dropped again.

Write min_drops(eggs, floors) that returns the smallest number of drops that is always enough to find s for certain, however unlucky the results are.

Examples

min_drops(1, 10)   # returns 10
min_drops(2, 10)   # returns 4
min_drops(2, 100)  # returns 14
min_drops(3, 0)    # returns 0

With one egg you cannot take risks: you must try floors 1, 2, 3 and so on in order, so 10 floors can need 10 drops. A second egg lets you start higher and save drops.

Constraints

• 1 <= eggs <= 10
• 0 <= floors <= 500