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: X1 + X2 + · · · + Xp = n Then she asks Xavier put p cards on the corresponding Xi’s position to make this equation correct, with an additional condition that Xi should be ordered from smaller to bigger, i.e. Xi <Xi+1, ∀i, 1≤<p 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. Sample Input 3 33 123 54 13567 10 3 1 2 3 4 5 6 7 8 9 10 Sample Output Case #1: 6: 1
2/2 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