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.