1010 Radix

1010 Radix (25)（25 分）

Given a pair of positive integers, for example, 6 and 110, can this

equation 6 = 110 be true? The answer is "yes", if 6 is a decimal number

and 110 is a binary number.

Now for any pair of positive integers N1 and N2, your task is to find

the radix of one number while that of the other is given.

Input Specification:

Each input file contains one test case. Each case occupies a line which

contains 4 positive integers:\

N1 N2 tag radix\

Here N1 and N2 each has no more than 10 digits. A digit is less than its

radix and is chosen from the set {0-9, a-z} where 0-9 represent the

decimal numbers 0-9, and a-z represent the decimal numbers 10-35. The

last number "radix" is the radix of N1 if "tag" is 1, or of N2 if "tag"

is 2.

Output Specification:

For each test case, print in one line the radix of the other number so

that the equation N1 = N2 is true. If the equation is impossible, print

"Impossible". If the solution is not unique, output the smallest

possible radix.

Sample Input 1:

6 110 1 10

Sample Output 1:

2

Sample Input 2:

1 ab 1 2

Sample Output 2:

Impossible

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