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E |
Simple
Encryption Input: Standard Input Output: Standard Output |
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Some day in the future a person
named Reuben wants to submit some interesting problems to the judging director
of ACM ICPC (Association for Copotron Mechanics International Collegiate
Programming Contest) World Finals so that they can be used in World Finals
2031. This contest requires problem submitters to submit their problems in
encrypted format. But in year 2030, encryption software is not
widely available on the Internet just to prevent terrorists from sending
encrypted messages. So he wants to use a simplified encryption technique to
submit his problem. He uses several 12-digit encryption keys to encrypt his
messages. We would not disclose the encryption/decryption technique for safety
because your next generations will be competing in World Finals by then. But
Reuben also does not want to send his encryption key in a straightforward
email. He wants to send a key (public) K1 that will implicitly
denote the actual key (private) K2. K2 is
such a 12 digit number so that 
(modulo 1012).
Given the value of K1 your job is to help Reuben find the
value of K2.
Input
The input file contains around 1600
line of input. Each line contains an integer, which denotes the value of K1
(0<K1<50001). A line containing a single zero terminates
input.
Output
For each
line of input produce one line of output. This line contains the serial of
output, followed by the given public key K1 and
then a possible actual private key K2. Look at the output for
sample input for exact formatting. Inputs will be such that for given value of K1
there will always be at least one value of K2.
Note that K2 should always have 12 digits and will not
have any leading zeroes.
Sample
Input Output for Sample Input
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78 99 0 |
Case
1: Public Key = 78 Private Key = 308646916096 Case
2: Public Key = 99 Private Key = 817245479899 |
Problemsetter: Shahriar
Manzoor, Special Thanks: Derek Kisman