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Number System Converter
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.
The input contains several test cases. The first line of each test case specifies two number P and Q (1 < P < Q < 37), follow by N0 (the length of N0 is not larger than 5,000,000). Note that a digit larger than 9 is given in small letters, with 'a'=10, 'b'=11 ...
For each test case, output a line standing for the final sequence in the circuit.
2 4 321
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