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单点时限: 1.0 sec
内存限制: 256 MB
In a strange shop there are $n$ types of coins of value $A_1, A_2, \ldots, A_n$. 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:
So, 5 can be made in 4 ways.
Input starts with an integer $T$ ($T \le 20$), denoting the number of test cases.
Each case starts with a line containing two integers $n$ ($1 \le n \le 100$) and $K$ ($1 \le K \le 100~000$). The next line contains $n$ integers, denoting $A_1, A_2, \ldots, A_n$ ($1 \le A_i \le 100~000$). 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 $100~000~007$.
2 3 5 1 2 5 4 20 1 2 3 4
Case 1: 4 Case 2: 108