**Challenge 11** - All the Possibilities

Some people in the office are thinking about how many possible addition operations can be obtained given a positive number. Taking some considerations like A + B = B + A and only one of them should be summarized. Furthermore, A > 0 && B > 0.

### Input

On the first line, an integer T indicates the number of cases. Each case is described on a line with an integer **X**
, which is the value to obtain, and a list of **M** positive numbers **N _{0}, N_{1}... N_{M-1}**
separated by an empty space. These values cannot be used to calculate the operations.

### Output

For each case T, the output should be the string "Case #t:" followed by the total possible operations. See the example output.

### Limits

- 1 ≤
**T**≤ 100 - 1 ≤
**X**≤ 100 - 0 ≤
**M**≤ 100 - 1 ≤
**N**<_{0}, N_{1}... N_{M-1}**100**

### Sample Input

2 2 1 5 4 2

### Sample Output

Case #1: 0 Case #2: 2

In the first case (2), there are no way to summarize 2 without the operand 1.

The second case (5) can be calculate with the operations **1+3+1** and **1+1+1+1+1**, so there are 2 possible
operations.

### Problem stats

Completion time: |
min: 0:09:58 h10th percentile: 0:38:36 h90th percentile: 22:37:47 hmax: 76:26:43 h |
---|---|

Test phase time: |
10th percentile: 0:28:20 h90th percentile: 14:45:05 h |

Submit phase time: |
10th percentile: 0:01:07 h90th percentile: 9:19:02 h |

# of completions: | 139 |