You are given two non-decreasing sequences $A = (A_1, A_2, ..., A_M)$ and $B = (B_1, B_2, ..., B_N)$.

You can choose any two indices $i$ and $j$, and then swap $A_i$ and $B_j$.

Note that the you can do the operations as many times as you want, and your goal is to transform $A$ into an arithmetic sequence. After opeartions, you can rearrange the sequence $A$.

Now, determine how many distinct arithmetic sequences you can obtain.

Input Format

• The first line contains a single integer $T$ — the number of test cases.
• For each testcase:
  • The first line contains two integer $M$ and $N$ — the lengths of the sequences $A$ and $B$, respectively.
  • The second line contains $M$ integers $A_1, A_2, ..., A_M$.
  • The third line contains $N$ integers $B_1, B_2, ..., B_N$.

Output Format

• For each testcase, output the number of distinct arithmetic sequences you can obtain.

Constraints

• $1 \leq T \leq 10^3$
• $2 \leq N \leq M \leq 10 ^ 5$
• $-M \leq A_i, B_j \leq M$
• The sum of $M + N$ across all test cases does not exceed $2 \cdot 10 ^ 7$.