A, B, C and D were arrested on suspicion of theft from a jewelry store.  The statements of the four are as follows: A: The perpetrator is C.  B: Ding is the criminal. C: If I commit the crime, Ding is the principal criminal.  D: I did not commit the crime.  Only one of the four statements is false.
 It was A who lied and B who committed the crime is true if the above is true.