Soupy boy is playing a game! He is currently on the ~N^{th}~ square, and wants to get to the ~M^{th}~ square exactly. However, moves in this game are a bit different than your average board game.

Starting from the current square, he can do one of ~4~ things.

• Go to the ~(3 \times N)^{th}~ square.
• Go to the ~(N-1)^{th}~ square.
• Go to the ~(N-3)^{th}~ square.
• Go to the ~(\dfrac{N}{2})^{th}~ square if the current square is even.

Can you tell soupy boy what is the minimum amount of moves so that he can get to the ~M^{th}~ square?

Note: You can assume that soupy boy will not go to a square that is larger than ~10^7~.

Input Specification

The first and only line of input contains the two integers ~N~ and ~M~ ~(1 \le N, M \le 10^5)~, separated by a space.

Output Specification

Output the minimum amount of moves it takes soupy boy to get to the ~M^{th}~ square, starting from the ~N^{th}~ square using the moves described above.

Sample Input 1

4 6

Sample Output 1

2

Sample Input 2

10 1

Sample Output 2

3