ACM Lab produced a batch of number system converter recently. There are two kind of converter R1 and R2.

Given a parameter of P, converter R1's function is to transform the incoming P based integer into decimal number system. To simplify the design, R1 will not check that if the input is legal in P number system.

R2 is similar to R1, while acting an inverse function: convert a decimal number to Q(specified by R2) number system.

H.X.Q, a researcher of ACM Lab, made a circuit uses R1 and R2:

(The circuit works at an order R1, R2, R1, R2 ...)

And she found an interesting phenomenon: if P<Q then for any input sequence N0, after plenty of convention N1 will finally equal to N2. For example, P=2, Q=4, N0=321, finally, N1=N2=3.

H.X.Q is excited for her discover, and wants to know what N1 and N2 will finally be in this circuit when P, Q and N0 is given.