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1232 - Coin Change (II)
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Time Limit: 1 second(s) Memory Limit: 32 MB

In a strange shop there are n types of coins of value A1, A2 ... An. You have to find the number of ways you can make K using the coins. You can use any coin at most K times.

For example, suppose there are three coins 1, 2, 5. Then if K = 5 the possible ways are:

11111

1112

122

5

So, 5 can be made in 4 ways.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing two integers n (1 ≤ n ≤ 100) and K (1 ≤ K ≤ 10000). The next line contains n integers, denoting A1, A2 ... An (1 ≤ Ai ≤ 500). All Ai will be distinct.

Output

For each case, print the case number and the number of ways K can be made. Result can be large, so, print the result modulo 100000007.

Sample Input

Output for Sample Input

2

3 5

1 2 5

4 20

1 2 3 4

Case 1: 4

Case 2: 108

 


Problem Setter: Jane Alam Jan
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