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 Specification

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

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 of Sample

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.