Problem Statement 
 Let's consider an infinite sequence S of nonnegative integers defined as follows:
S_{0} = first;
S_{1} = second;
S_{i} = S_{i2}  S_{i1} for all i >= 2.
You will be given Strings first and second, representing the 0th and the 1st elements of the sequence S, and a String[] indices, each element of which represents a nonnegative integer without extra leading zeros. Return a String[] containing as many elements as indices, where the ith element is equal to the indices[i]th element of the sequence S (index is 0based). No element of the return should contain extra leading zeros. 

Definition 
 Class:  AbsSequence  Method:  getElements  Parameters:  String, String, String[]  Returns:  String[]  Method signature:  String[] getElements(String first, String second, String[] indices)  (be sure your method is public) 




Constraints 
  first will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros. 
  second will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros. 
  indices will contain between 1 and 50 elements, inclusive. 
  Each element of indices will represent an integer between 0 and 10^18, inclusive, with no extra leading zeros. 

Examples 
0)  
 "21"  "12"  {"0", "1", "2", "3", "4"} 
 Returns: {"21", "12", "9", "3", "6" }  Here S_{0}=21 and S_{1}=12. The next three sequence elements are S_{2} = 21  12 = 9, S_{3} = 12  9 = 3 and S_{4} = 9  3 = 6. 


1)  
 "0"  "0"  {"1000000000000000000"} 
 Returns: {"0" }  Here we get the sequence consisting of only zeros. 


2)  
 "823"  "470"  {"3","1","31","0","8","29","57","75","8","77"} 
 Returns: {"117", "470", "2", "823", "115", "87", "49", "25", "115", "23" }  

3)  
 "710370"  "177300"  {"5","95","164721","418","3387","710","0","1197","19507","5848"} 
 Returns: {"178470", "108270", "90", "0", "90", "90", "710370", "90", "0", "0" }  
