Catch the Cow

Problem Description

A farmer knows where a cow is and wants to catch it. The farmer and the cow are on a number line. The farmer starts at position $N$ ($0 \le N \le 100000$) and the cow is at $K$ ($0 \le K \le 100000$). The farmer has two kinds of moves:

1. move from $X$ to $X-1$ or $X+1$, taking one minute;

2. move from $X$ to $2X$, taking one minute.

Assume the cow does not notice the farmer and stays still. What is the minimum time the farmer needs to catch the cow?

Input Format

Two integers, $N$ and $K$.

Output Format

One integer: the minimum number of minutes needed to catch the cow.

Sample Input

5 17

Sample Output

4

Limitation

1 s, 1024 KiB for each test case.