University Exam#11781
A professor at a university in Zhytomyr is conducting an exam for a group of students, all of whom have the same level of knowledge.
The professor is in a hurry and wants to evaluate his students' knowledge in the shortest possible time. Therefore, the professor has prepared problems, the difficulty level of which he has rated from to points. All problems have different levels of difficulty. A student's level of knowledge is assessed at points if they can solve a problem with a difficulty level of , but cannot solve a problem with a difficulty level of R+1.
It is considered that if a student fails to solve a problem, then they will not be able to solve any other problem of a higher level of difficulty. If a student solves a problem, they can solve any lower-level problem. If they cannot solve a problem of difficulty level , their knowledge is assessed at points. If the student solves a problem of difficulty level , they receive points.
The exam itself is conducted as follows: the professor selects a problem and gives it to the student. If the student solves it within minute, the professor gives them another problem. If not, the student leaves the room.
Write a program that answers the question: what is the minimum time (in minutes) the professor needs to guaranteed determine the knowledge level of his students?
The first line contains the numbers and separated by a space (1 \leq K \leq 100, 1 \leq N \leq 1000).
A single number - the result.
Example 1
In this case, the student is offered a problem of difficulty level . If they do not solve it, the next student is offered a problem of difficulty level , otherwise the first student is offered a problem of difficulty level