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

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