CODE1  Secret Code
The Sarcophagus itself is locked by a secret numerical code. When somebody wants to open it, he must know the code and set it exactly on the top of the Sarcophagus. A very intricate mechanism then opens the cover. If an incorrect code is entered, the tickets inside would catch fire immediately and they would have been lost forever. The code (consisting of up to 100 integers) was hidden in the Alexandrian Library but unfortunately, as you probably know, the library burned down completely.
But an almost unknown archaeologist has obtained a copy of the code something during the 18th century. He was afraid that the code could get to the ``wrong people'' so he has encoded the numbers in a very special way. He took a random complex number B that was greater (in absolute value) than any of the encoded numbers. Then he counted the numbers as the digits of the system with basis B. That means the sequence of numbers a_{n}, a_{n1}, ..., a_{1}, a_{0} was encoded as the number X = a_{0} + a_{1}B + a_{2}B^{2} + ...+ a_{n}B^{n}.
Your goal is to decrypt the secret code, i.e. to express a given number X in the number system to the base B. In other words, given the numbers X and Byou are to determine the ``digit'' a_{0} through a_{n}.
Input
The input consists of T test cases (equal to about 100000). The number of them (T) is given on the first line of the input file. Each test case consists of one single line containing four integer numbers X_{r}, X_{i}, B_{r}, B_{i} (X_{r},X_{i} <= 1000000, B_{r},B_{i} <= 16). These numbers indicate the real and complex components of numbers X and B, i.e. X = X_{r} + i.X_{i}, B = B_{r} + i.B_{i}. B is the basis of the system (B > 1), X is the number you have to express.
Output
Your program must output a single line for each test case. The line should contain the ``digits'' a_{n}, a_{n1}, ..., a_{1}, a_{0}, separated by commas. The following conditions must be satisfied:
 for all i in {0, 1, 2, ...n}: 0 <= a_{i} < B
 X = a_{0} + a_{1}B + a_{2}B^{2} + ...+ a_{n}B^{n}
 if n > 0 then a_{n} <> 0
 n <= 100
If there are no numbers meeting these criteria, output the sentence
"The code cannot be decrypted.
". If there are more possibilities,
print any of them.
Example
Sample Input 4 935 2475 11 15 1 0 3 2 93 16 3 2 191 192 11 12 Sample output: 8,11,18 1 The code cannot be decrypted. 16,15Warning: large Input/Output data, be careful with certain languages
hide comments
kemar:
20210917 18:02:15
It seems that the last line of the input data doesn't end with a '\n' but with a digit.


morino_hikari:
20170726 03:43:29
The key to this problem is trying to find out a recursive formula of the residual by moving the constant term from the right side to the left and then quotient both side with the 'complex base'. お大事に。


sourav2706:
20151028 15:54:20
can anybody help me regarding the algorithm used in this program


sourav2706:
20151028 15:51:10
its total mathematics


Priyanshu Gupta:
20150304 11:54:43
getting segmentation fault but not using any array or vector... any idea?


Georeth Chow:
20141211 14:49:29
Note the constraint:


BaburMB:
20131207 15:20:11
you can store as sqrt(123124) 

Aneeqa:
20130807 17:23:16
it looks like algorithm :p 

nilesh soni:
20120525 12:18:21
in every problem of spoj for int part of float no., simply x=int(x) does not accept


CryptoViral:
20120307 11:45:23
ha ha sqrt(1).......:D 
Added by:  adrian 
Date:  20040606 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACM Central European Programming Contest, Prague 1999 