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.

Input

Input is given from Standard Input in the following format:
X Y

Output

Print the answer.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分