## XC - Xavier is Learning to Count

Xavier, a 9-year-old student, loves playing many kinds of puzzles. One of his favourites is the following:

Xerier, his classmate, has made many cards. She writes down a single positive number on each of them. No numbers written on different cards are the same. After that she writes down an equation, whose right side is a single positive number chosen by her, and the left side is the sum of p integers:

Then she asks Xavier put p cards on the corresponding X_{i}'s position to make this equation correct, **with an additional condition that X _{i} should be ordered from smaller to bigger**, i.e.

Every time Xavier immediately comes up with many solutions. Now he wants to know how many solutions in total are there for any n given by Xerier.

### Input

There are multiple test cases. The number of them is given in the beginning of the input. Then a series of input block comes one by one.

For each test case:

The first line contains two space-separated integers m and p (1<=p<=5). The second line contains m distinct positive integers - the numbers written on each of the cards. None of these integers exceeds 13000.

There are about 120 test cases in total, but 90% of them are relatively small. More precisely, all numbers are less than or equal to 100 in 90% of the test cases.

### Output

For each test case:

For each positive integer, output the number of ways in a single line. To keep the output finite, only numbers with positive ways should be outputted.

Output a blank line after each test case. See sample for more format details.

### Example

Input:3 3 3 1 2 3 5 4 1 3 5 6 7 10 3 1 2 3 4 5 6 7 8 9 10Output:Case #1: 6: 1 Case #2: 15: 1 16: 1 17: 1 19: 1 21: 1 Case #3: 6: 1 7: 1 8: 2 9: 3 10: 4 11: 5 12: 7 13: 8 14: 9 15: 10 16: 10 17: 10 18: 10 19: 9 20: 8 21: 7 22: 5 23: 4 24: 3 25: 2 26: 1 27: 1

*This problem has 82 submissions during the onsite contest, but none of them gets Accepted.*

Added by: | Fudan University Problem Setters |

Date: | 2011-10-10 |

Time limit: | 7s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | ACM/ICPC Regional Contest, Shanghai 2011; Problem Setter: Blue Mary; Special Thanks: Gustav Matula |