Bob sells burgers with three different combinations, $$B_1$$, $$B_2$$ and $$B_3$$. There are total $$X$$, $$Y$$, and $$Z$$ burgers with combinations, $$B_1$$, $$B_2$$, and $$B_3$$ respectively. Each burger has an integer value called deliciousness as follows:

The deliciousness of the burgers with the $$B_1$$ combination are \(B_{11}, B_{12}, B_{13}, .... , B_{1X}\).
The deliciousness of the burgers with the $$B_2$$ combination are \(B_{21}, B_{22}, B_{23}, .... , B_{2Y}\).
The deliciousness of the burgers with the $$B_3$$ combination are \(B_{31}, B_{32}, B_{33}, .... , B_{3Z}\).

Alice decides to buy $$K$$ boxes containing three burgers, one from each of the combinations. The deliciousness of a box is the sum of the deliciousness of the burgers present inside it.

There are \(X*Y*Z\) such ways to select a box. Print the maximum total sum of deliciousness that Alice can get by buying $$K$$ boxes.

Input format

The first line contains an integer $$T$$ denoting the number of test cases.
The first line of each test case contains three space-separated integers $$X$$, $$Y$$, and $$Z$$.
The second line of each test case contains a single integer $$K$$.
The third line of each test case contains $$X$$ space-separated integers denoting array $$B_{1i}$$.
The fourth line of each test case contains $$Y$$ space-separated integers denoting array $$B_{2j}$$.
The fifth line of each test case contains $$Z$$ space-separated integers denoting array $$B_{3k}$$.

Output format

For each test case, print the maximum total sum of deliciousness that Alice can get by buying $$K$$ boxes in a new line.

Constraints

\(1 \le T \le 10\\ 1 \le X,Y,Z \le 1000\\ 1 \le K \le min(3000,X*Y*Z)\\ 1 \le B_{1i},B_{2j},B_{3k} \le 1000000000\)