Count the Polygons

Input: Standard Input

Output: Standard Output

A polygon is a plane figure that is bounded by a closed path and composed of a finite sequence of straight line segments. These segments are called its edges, and the points where two edges meet are the polygon's vertices.

You have got a set of N sticks of various lengths. How many ways can you choose K sticks from this set and form a polygon with K sides by joining the end points.

Input

The first line of input is an integer T (T<100) that indicates the number of test cases. Each case starts with a line containing 2 positive integers N and K ( 3≤N≤30 & 3≤K≤N ). The next line contains N positive integers in the range [1, 2^31), which represents the lengths of the available sticks. The integers are separated by a single space.

Output

For each case, output the case number followed by the number of valid polygons that can be formed by picking K sticks from the given N sticks.

Sample Input Output for Sample Input

4 3

10 10 20 20

6 4

1 1 1 1 1 1

4 3

10 20 30 100000000

6 6

2 3 4 5 6 7

Case 1: 2
Case 2: 15
Case 3: 0
Case 4: 1

Problem Setter: Sohel Hafiz

Special Thanks: Md. Arifuzzaman Arif