BURGLARY  Boat Burglary
Rachid lives on a boat, and owns only a few items, n to be precise. He takes big care of his items, and measured the weight of each of them with high precision. Item i weights W_{i} micrograms. One night a thief visits his boat and steels some items. Rachid notices that the next morning, because the boat is lighter, and he could measure from the water level that this difference is D micrograms. He would like to know how many items are missing, just by examining these weights, and asks you for help.
Input
The first line of the input consists of the number of test cases, T. T test cases follow. Each case consists of two lines, the first one containing two integers N and D, separated by a space. Then second line contains n integers, representing the weights of all items, separated by space.
The input satisfies the following limits.
1≤T≤20
1≤N≤30
0≤D≤3*10^{10}
0≤W_{i≤}10^{9}
Output
For each test case output one line containing "Case #x: y", where x is the case number (starting from 1). If the number of missing items could be determined, then y is this number. If there are several answers to the problem y is the string "AMBIGIOUS" and if there is no answer y is the string "IMPOSSIBLE" (quotes added for clarity and are not part of the output).
Example
Input: 4 5 10 2 3 6 9 5 5 20 1 4 2 3 15 5 20 1 4 5 15 27 5 16 1 2 4 8 32 Output: Case #1: 3 Case #2: 3 Case #3: AMBIGIOUS Case #4: IMPOSSIBLE
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thanhtungpfiev:
20210815 09:49:42
Input:


smso:
20180525 08:30:04
It should be AMBIGUOUS instead of AMBIGIOUS. 

abhishekpal:
20170404 11:21:37
Last edit: 20170405 11:23:10 

wisfaq:
20161103 09:58:11
Anybody out there ? Why don't I get an answer on a reasonable request?


wisfaq:
20161021 21:31:00
Would it be possible to raise the time limit to say 2 or 4 sec to make it possible that slow languages like Python can get AC? Last edit: 20161021 21:32:32 

Christoph Dürr:
20161012 10:46:06
Dear dwij28, I added the constraint on D. Indeed you can do all computations with 64 bits integers.


Poog:
20161011 11:54:36
My code, is running on Ideone.com (and get the right answer), but here i get SIGABRT on runtime, any hints? 

abhi2296:
20161010 06:51:32
Last edit: 20171027 08:43:59 

:D:
20161008 20:06:27
I assumed it fits into signed 64b integer. 

dwij28:
20161008 15:54:02
What is the constraint on D ? Last edit: 20161008 17:58:15 
Added by:  xtof 
Date:  20161006 
Time limit:  1s4s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 GOSU 
Resource:  http://acm.tju.edu.cn/toj/showp4095.html 