Background

Mathematicians’ virtue of seeking the beauty of truth, the source of unceasing strength — courage.

Joy, “Light of Courage”, is the succeeding chief of the Dwarf族 (Duwofu, pinyin), and also a warrior who possesses the power of the ancient God of War.

Problem Description

Joy has a skill that can strengthen an attack power of $x$ into $x^2$. However, this skill is not perfect: except for the first time, before each use of the skill, the attack power will decay to half of the previous value.

For example, if the initial attack power is $\color{red}6$, after strengthening it becomes $6^2=\color{red}{36}$. Before the next strengthening, it will first decay to $36/2=18$, and then be strengthened into $18^2=\color{red}{324}$.

Joy wants to know: if the initial attack power is $x$, what is the minimum number of strengthenings needed to make it not less than $2^n$?
If no matter how many times it is strengthened, it is still impossible to meet the requirement, output inf.

Input Format

One line containing two positive integers $x,n$, representing the initial attack power $x$ and the target attack power $2^n$.

Output Format

Output one line with one integer or the string inf, representing the answer.

2 1

0

3 6

3

16 335

7

Hint

[Sample $1$ Explanation]
The initial attack power $x=2$ already reaches $2^n=2$, so it satisfies the requirement without using the skill. Therefore the answer is $0$.

[Sample $2$ Explanation]
The initial attack power is $3$, and the target is $2^6=64$. After the first use it becomes $9$, after the second it becomes $(9/2)^2=81/4$, and after the third it becomes $((81/4)/2)^2=6561/64$, which already meets the requirement. Therefore the answer is $3$.

[Constraints]
This problem uses bundled testdata.

Subtask 1 (15 pts): $n\le 60$.
Subtask 2 (20 pts): $x=4$.
Subtask 3 (25 pts): $n\le 10^5$.
Subtask 4 (40 pts): no special constraints.

For all testdata: $2\le x\le 10^9$, $1\le n \le 10^9$.

Translated by ChatGPT 5