Problem Description
In the game "Gem Craft", we create gems in the item bar.
There are N grids in the item bar, each grid can only accomodate one gem.
Each gem has its level.
When the level of a gem upgrade by 1, the power of the gem will be doubled.
The key to win the game is to get a high level gem.
Gems with level 0 are available directly.
To get gems with higher level, the only way is to combine low level gems.
Suppose we have 2*N gems with level K now, they can be turned into N gems with level (K+1) afert a combining operation.
Your task is to get at least one gem with level M in minimum steps of operation.
For one step of operation, you can do one of the following two things:
(1) Get gems with level 0 directly, filling up the empty grids.
(2) Combine even number of gems with same level.
Input
The input contain some test cases.
Each test case contains two integers N and M (1<=N<=36, 0<=M<=20).
The input ends when N=M=0, this test case doesn't need processing.
Output
For each test case, output one line.
The line contains only one integer, the minimum steps of operation.
If there is no solution to get a gem with level M, output -1 instead.
Sample Input
4 3
8 3
0 0
Sample Output
9
4
Hint
We use dots to present empty grid, use number to present the level of a gem.
The first sample can be solved like this:
**** Initial
0000 Get level 0 gems
**11 Combine level 0 gems
***2 Combine level 1 gems
0002 Get level 0 gems
012 Combine level 0 gems
0012 Get level 0 gems
*112 Combine level 0 gems
**22 Combine level 1 gems
**3 Combine level 2 gems
In total of 9 steps of operation.
The second sample can be solved like this:
******** Initial
00000000 Get level 0 gems
****1111 Combine level 0 gems
******22 Combine level 1 gems
*******3 Combine level 2 gems
It only takes 4 steps of operation.
