You are given two integers, $a$ and $b$. You want to transform $a$ to $b$ by performing a sequence of operations. You can only perform the following operations:
 - Divide $a$ by two (only if $a$ is even)
 - Add one to $a$

What is the minimum number of these operations you need to transform $a$ into $b$?

-----Input-----
The single line of input contains two space-separated integers $a$ and $b$ ($1\le a,b \le 10^9$). You want to transform $a$ into $b$ using only the operations given above.

-----Output-----
Output a single integer, which is the minimum number of the given operations needed to transform $a$ into $b$.

-----Examples-----
Sample Input:
103 27
Sample Output:
4

Source: kattis | Difficulty: EASY


Solutions: