In a strange shop there are n types of coins of value A₁, A₂ ... A_n. 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:

1. (1, 1, 1, 1, 1)
2. (1, 1, 1, 2)
3. (1, 2, 2)
4. (5)

So, 5 can be made in 4 ways.

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 ... A_n (1 ≤ A_i ≤ 500). All A_i will be distinct.

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.