You are given $2$ integers arrays $A$ and $B$ of size $N$, for every index $i$, you could either add $B_i$ to $A_i$ or subtract $B_i$ from $A_i$, you are only allowed to do atmost $K$ add operations. For a subarray of size $L$ print the largest possible sum after doing the above operations.

Input format

• The first line contains $T$, denoting the number of test cases.
• First line of each test case contains $N,L,K$ denoting the size of the array, length of the subarray and the number of operations.
• Then the next line contains $N$ integers, denoting the element of array $A$.
• Then the next line contains $N$ integers, denoting the element of array $B$.

Output format

• Print a integer denoting the largest possible sum after doing the above operations

Constraints

$1 \le N \le 10^5$

$1 \le K \le L \le N$

$-10^9 \le A_i,B_i \le 10^9$

The sum of $N$ over all test case does not exceed $2 \cdot 10^5$