Suppose that a high-level language H is compiled into an intermediate language I, which in turn is compiled into a native machine language M. These three languages can be executed by a virtual or a hardware machine, yielding six execution methods. For each of the following pairs, indicate which method is faster in execution speed: 

a. virtual machine for H vs. hardware machine for I 

b. virtual machine for H vs. virtual machine for M 

c. virtual machine for I vs. hardware machine for M 

d. hardware machine for I vs. virtual machine for I 

e. hardware machine for M vs. hardware machine for H