It’s universally acknowledged that there’re innumerable trees in the campus of HUST.  
      And there are many different types of trees in HUST, each of which has a number represent its type. The doctors of biology in HUST find 4 different ways to change the tree’s type x into a new type y: 
   1.    y=x+1 
   2.    y=x-1 
   3.    y=x+f(x) 
   4.    y=x-f(x)  
   The function f(x) is defined as the number of 1 in x in binary representation. For example, f(1)=1, f(2)=1, f(3)=2, f(10)=2.  
   Now the doctors are given a tree of the type A. The doctors want to change its type into B. Because each step will cost a huge amount of money, you need to help them figure out the minimum steps to change the type of the tree into B.  
   
   
   Remember the type number should always be a natural number (0 included).