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 $A_1, A_2, \ldots, A_n$. $C_1, C_2, \ldots, C_n$ denote the number of coins of value $A_1, A_2, \ldots, A_n$ respectively. You have to find the number of ways you can make $K$ using the coins.
For example, suppose there are three coins $1, 2, 5$ and we can use coin $1$ at most $3$ times, coin $2$ at most $2$ times and coin $5$ at most $1$ time. Then if $K = 5$ the possible ways are:
So, 5 can be made in 3 ways.
Input starts with an integer $T$ ($T \le 10$), denoting the number of test cases.
Each case starts with a line containing two integers $n$ ($1 \le n \le 100$) and $K$ ($1 \le K \le 10~000$). The next line contains $2n$ integers, denoting $A_1, A_2, \ldots, A_n, C_1, C_2, \ldots, C_n$ ($1 \le A_i \le 100~000, 1 \le C_i \le 1~000$). 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 3 2 1 4 20 1 2 3 4 8 4 2 1
Case 1: 3 Case 2: 9