uva1101測資A

Input:
1 2 2 3 10 20
1 3 2 3 22 33
3 2 2 3 4 5
5 3 2 3 2 3
2 4 12 14 20 30
7 9 23 35 23 35
7 9 22 35 23 35
2 4 4 8 20 40
4 2 2 4 40 50 
6 4 4 8 10 20
5 10 4 8 100 120 
10 5 2 4 100 120
11 14 35 78 1999 2005
4 2 4 8 400 1000
6 4 22 24 6000 10000
4 6 32 64 8002 8010
4 6 4 8 900000 1000000
5 10 2 4 100000 300000
10 5 22 34 1000 1200
10 5 10 500 100000 120000
10 5 2 4 1000000 1200000
144 123 834 3453 1293923 234738234
4 12 83 343 834730000 834738234
3 5 6 7 123456789 987654321
3 4 8 9 999990000 999999999
2 3 4 5 999950000 999990000
3 2 4 5 999950000 999990000
0 0 0 0 0 0
Output:
Case 1: 1A 2M
Case 2: 1M 2A 1M
Case 3: impossible
Case 4: empty
Case 5: 4A
Case 6: empty
Case 7: impossible
Case 8: 1A 1M
Case 9: 2A 2M
Case 10: 1A
Case 11: 20A
Case 12: 2A 1M
Case 13: impossible
Case 14: 1A 6M
Case 15: 1A 4M
Case 16: impossible
Case 17: 28A 5M
Case 18: 2A 4M
Case 19: 18A 1M
Case 20: 399A 2M
Case 21: 1A 2M 2A 5M
Case 22: 2M
Case 23: 17390188A 1M
Case 24: 11M
Case 25: 81377A 6M
Case 26: 25399A 1M 2A 8M
Case 27: 10170A 1M 1A 1M 1A 13M