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

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