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1122 - Digit Count
  PDF (English) Statistics Forum
Time Limit: 2 second(s) Memory Limit: 32 MB

Given a set of digits S, and an integer n, you have to find how many n-digit integers are there, which contain digits that belong to S and the difference between any two adjacent digits is not more than two.

Input

Input starts with an integer T (≤ 300), denoting the number of test cases.

Each case contains two integers, m (1 ≤ m < 10) and n (1 ≤ n ≤ 10). The next line will contain m integers (from 1 to 9) separated by spaces. These integers form the set S as described above. These integers will be distinct and given in ascending order.

Output

For each case, print the case number and the number of valid n-digit integers in a single line.

Sample Input

Output for Sample Input

3

3 2

1 3 6

3 2

1 2 3

3 3

1 4 6

Case 1: 5

Case 2: 9

Case 3: 9

Note

For the first case the valid integers are

11

13

31

33

66


Problem Setter: Jane Alam Jan
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