You are given two arrays $A$ and $B$ of length $N$ and $M$ respectively. You can perform the following operation any number of times on $A$ and $B$.

• Replace any subarray of the array with the sum of the elements in the subarray.

You want to make $A$ and $B$ equal. Find the maximum possible length of arrays $A$ and $B$ such that $A$ is equal to $B$. If it is impossible to make $A$ and $B$ equal then print $-1$.

Input format

• The first line contains an integer $T$, which denotes the number of test cases.
• The first line of each test case contains two integers $N$ and $M$, denoting the length of the array $A$ and $B$.
• The second line of each test case contains $N$ space-separated integers, elements of array $A$.
• The third line of each test case contains $M$ space-separated integers, elements of array $B$.

Output format

For each test case, print the maximum possible length of arrays $A$ and $B$ such that $A$ is equal to $B$. If it is impossible to make $A$ and $B$ equal then print $-1$ in a new line.

Constraints

$1 \leq T \leq 10 \\ 1 \leq N, M \leq 10^5 \\ 1 \leq A[i], B[i] \leq 10^5$