Consider a strictly-increasing sequence of integers $a_1, a_2, \dots, a_k$. Alice picked a continuous sequence $p_1, p_2, \dots, p_n$ from it.

Bob then removed exactly $n-m$ numbers from this sequence, while maintaining the relative order of the remaining elements, thus obtaining a sequence $q_1, q_2, \dots, q_m$. He then subtracted $q_1$ from all the elements to form the final sequence $b_1, b_2, \dots, b_m$.

For example, let $\{a_i\} = \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31\}, p_1 = 11, n = 6, m = 4$. This yields the sequence of primes $p=\{11, 13, 17, 19, 23, 29\}$. Assume that Bob has removed the numbers 17 and 23 to obtain $q=\{11, 17, 19, 29\}$. After that, he subtracted 11 from every element to get $b=\{0, 6, 8, 18\}$.

Alternatively, he could have removed 11 and 29 to obtain the sequence $q = \{13, 17, 19, 23\}$ and $b = \{0, 4, 6, 10\}$. Note that the same sequence may also be generated by, for instance, picking $p = \{13, 17, 19, 23, 29, 31\}$ and removing 29 and 31.

Eve found the number $n$ and the sequences $\{a_i\}_{i=1}^{k}$, $\{b_i\}_{i=1}^{m}$. She now wonders, what is the smallest possible $p_1$, that could yield the sequence $\{b_i\}_{i=1}^{m}$ through the process described above?

Input format:

• First line: $t$ (number of test cases)
• For each test case
  • First line: Three space-separated integers $k$,  $n$, and $m$ satisfying $1 \leq m \leq n \leq k$
  • Second line: $k$ space-separated integers $\{a_i\}_{i=1}^k$ satisfying $0 \leq a_i \leq 10^9$ and $a_i < a_{i+1}$
  • Third line: $m$ space-separated integers $\{b_i\}_{i=1}^m$. It is guaranteed that $b_1 = 0$ .

It is guaranteed that there always exists a solution.

Output:

For each test case, output a single integer $p_1$ - the smallest element in the sequence that Alice chose.

Scoring:

In all test sets, $1 \leq t \leq 10$.

In the first test set, worth 12 points, $1 \leq m = n \leq 10^2$ and $k \leq 10^4$.

In the second test set, worth 21 points, $1 \leq m < n \leq 10^2$ and $k \leq 10^4$.

In the third test set, worth 24 points, $1 \leq m = n \leq 10^5$ and $k \leq 2*10^5$.

In the fourth test set, worth 25 points, $1 \leq m \leq n \leq 10^5$, $n - m \leq 50$ and $k \leq 2*10^5$.

In the fifth test set, worth 18 points,$t=3$, $1 \leq m \leq n \leq 5*10^5$, $n - m \leq 100$ and $k \leq 10^6$.