## BASECVT - Base Conversion (Easy)

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We want to make some base-conversion experiments. Here you can try basic methods.

### Input

The first line of input contains three integers T, the number of test cases, B1, the first base, B2, the second base.
Follow 2×T lines.
For each test case, on the first line your are given one integer k.
On the second line you are given k integers : the digits of N in base B1.

N = a0×B10 + ... + ai×B1i + ... + ak-1×B1k-1

### Output

For each test case, you have to print the number N in base B2. See sample for details.

### Example

```Input:
1 10 100
5
5 4 3 2 1
```
```Output:
3            <--- Don't forget the length of N in base B2 ;-)
45 23 1
```

### Explanations

For the lonely case, N = 5×100 + 4×101 + 3×102 + 2×103 + 1×104 = 12345.
We have: N = 45×1000 + 23×1001 + 1×1002. You have to print 3, the number of digits, then the digits: 45, 23 and 1.

### Constraints

```0 < T <= 200
1 < B1,B2 <= 10^9
1 < k <= 1000
0 <= ai < B1  , ak-1>0
```

If you find the constraints too easy, then you should try BASECONV.
The basic solution should give AC in 1.56s with Python3. (Edit 2017-02-11 : 0.42s with new compiler)
Have fun ;-)

hide comments :.Mohib.:: 2015-06-27 00:51:27 In explaination: N should be N = 45×100^0+ 23×100^1+ 1×100^2 =(Francky)=> Fixed ; thanks. Last edit: 2015-06-27 10:32:20 Mitch Schwartz: 2014-03-19 21:16:02 It seems my basic solution is more basic than your basic solution. :p --ans(Francky)--> No, mine is simpler. But funny you're right. Simple = (B1 -> binary -> B2). Good luck ;-) Edit : Don't forget to print the length in first line. And I'll increase the time limit. (Mitch) Thanks, you're right, that is a bit simpler. :) Last edit: 2014-03-19 21:55:48

 Added by: Francky Date: 2014-03-19 Time limit: 60s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 Resource: Own Problem