Problem

Rosie hates nothing more than carrying change. As a result, whenever she goes shopping she uses the opportunity to get rid of as much change as she can. She does this as follows:

1. Her total comes out to $K$ cents
2. She gives the grocer $K + L$ cents
3. The grocer gives back $L$ cents in the most efficient manner possible

For example, if Rosie is in Canada, her total is $K=60$, and Rosie has $4$ nickels and $3$ quarters, she can give the grocer $4$ nickels and two quarters ($K+L=70$). The grocer would then give her a dime ($L=10$ in change. This way, Rosie is able to get rid of $5$ coins, leaving her with $2$ in total.

Rosie has perfected this technique for Canada, however she loves to travel and wants to maximize her coin lossage everywhere. Given the $N$ types of coins the grocer has (assume the grocer has more than enough of every coin), the $M$ coins that Rosie has, and her total $K$, find the minimum number of coins she can have after the transaction.

Input

The first line of the input provides the number of test cases, $T (1 \leq T \leq 100)$. $T$ test cases follow. Each test case begins with three integers $N$, M, K (1 \leq N,M \leq 100,1 \leq K \leq 1\,000)$$.

The next line contains $N$ integers, the types of coins that the grocer has. Each of the grocer’s coins will have a value that is less than $10\,000$ and the grocer is able to give out any amount of change.

The line after that contains $M$ integers, the coins that Rosie has (she has one of each). The total value of all her coins will be between $K$ and $10\,000$.

Note: For the first 50% of cases, M=1.

Output

For each test case, your program should output one integer: the minimum number of coins that Rosie can have after the transaction.

Sample Input

2
5 7 60
5 10 25 100 200
5 5 5 5 25 25 25
5 1 100
1 9 12 19 24
200

Sample Output

2
5

Explanation for Sample Output

The first case is described in the problem statement. In the second case, Rosie has no choice except to give grocer her $200$ coin. Then, the grocer optimally gives her $100$ cents in change using three $24$ coins, one $19$ coin and one $9$ coin. Hence, Rosie is left with $5$ coins.