# Secret Code

Source : ACM ICPC Central European Regional 1999 |
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Time limit : 5 sec |
Memory limit : 32 M |

**Submitted** : 262, **Accepted** : 108

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`, ...,

_{n-1}`a`,

_{1}`a`was encoded as the number

_{0}`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 `B`you are to determine
the ``digit'' `a _{0}` through

`a`.

_{n}**Input Specification**

The input consists of `T` test cases.
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`). These numbers indicate the real and complex components of numbers

_{r}|,|B_{i}| <= 16`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 Specification**

Your program must output a single line for
each test case. The line should contain the ``digits''
`a _{n}`,

`a`, ...,

_{n-1}`a`,

_{1}`a`, separated by commas. The following conditions must be satisfied:

_{0}- 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.

**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. 16,15