101885: [AtCoder]ABC188 F - +1-1x2

Problem Statement

Takahashi has written an integer $X$ on a blackboard. He can do the following three kinds of operations any number of times in any order:

• increase the value written on the blackboard by $1$;
• decrease the value written on the blackboard by $1$;
• multiply the value written on the blackboard by $2$.

Find the minimum number of operations required to have $Y$ written on the blackboard.

Constraints

• $1 \le X \le 10^{18}$
• $1 \le Y \le 10^{18}$
• $X$ and $Y$ are integers.

Input

Input is given from Standard Input in the following format:

$X$ $Y$

Output

Print the answer.

Sample Input 1

3 9

Sample Output 1

3

Initially, $3$ is written on the blackboard. The following three operations can make it $9$:

• increase the value by $1$, which results in $4$;
• multiply the value by $2$, which results in $8$;
• increase the value by $1$, which results in $9$.

Sample Input 2

7 11

Sample Output 2

3

The following procedure can make the value on the blackboard $11$:

• decrease the value by $1$, which results in $6$;
• multiply the value by $2$, which results in $12$;
• decrease the value by $1$, which results in $11$.

Sample Input 3

1000000000000000000 1000000000000000000

Sample Output 3

0

If the value initially written on the blackboard equals $Y$, print $0$.