Clark and Harry are siblings. As they had been rivals since their early childhood, their father decided that
both should concentrate on a different sport when they were thirteen. That way, they would not have to
compete for success. Now both are twenty years old and excel in different fields: Clark plays chess while
Harry participates in dart-tournaments.
Having won a series of three tournaments in a row, Harry started teasing Clark about not having as much
success. Clark retorted that chess was less luck-based and thus more difficult. That offended Harry and led
him to the reply that in order to play darts optimally, a lot of combinatorics are necessary. Clark returned an
icy smile and the comment that memorizing all different late-games could hardly be called “combinatorics”.
This is how it came to the wager. Harry bets that he can find all possible late-games for generalized
dart-boards where memorized late-games do not help him. When Clark showed him a list of possible dart-
boards, Harry had to admit that he probably bit off more than he can chew. As his friend, you have to help
him!
A dart-board consists of different areas. Each area has an assigned score for hitting it. Each area also has
a double- and a triple-field that are worth twice and three times the score of the area. The only exception
is the area for the highest score: It has only a double- and no triple-field! Given the values of the different
areas you have to find the number of possible scores that can be obtained with a given number of darts.
Input
The inputs start with a line containing a single integer n. Each of the n following lines contains one test
case. Each test case starts with two integers 1 ≤ a ≤ 100, 1 ≤ k ≤ 50, the number of different areas on the
dart-board and the number of darts. a integers 1 ≤ si ≤ 100 follow. si is the score for hitting area i. All
scores are distinct. Remember that each area has a double- and, with exception of the area with the highest
score, a triple-field. It is always possible to score 0 with any given dart by not hitting the board.
Output
The output for every test case begins with a line containing “Scenario #i:”, where i is the number of
the scenario counting from 1. After that, output a single line containing the number of different scores that
can be obtained with k darts on the given board. Terminate each test case with an empty line.