D. An Alternative Way
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two arrays $$$a$$$ and $$$b$$$, each of length $$$n$$$. You are allowed to perform the following operation on array $$$a$$$ any number of times (including zero):

  1. Choose two indices $$$l$$$ and $$$r$$$ such that $$$1 \le l \le r \le n$$$;
  2. For each index $$$i$$$ from $$$l$$$ to $$$r$$$ (both inclusive),
    • Set $$$a_i := a_i - 1$$$ if $$$i - l$$$ is odd.
    • Set $$$a_i := a_i + 1$$$ if $$$i - l$$$ is even.

Determine whether you can make the array $$$a$$$ equal to the array $$$b$$$ by performing the operation any number of times.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Description of each test case follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2\cdot10^5$$$) — the length of the arrays $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the elements of the array $$$a$$$.

The third line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \le b_i \le 10^9$$$) — the elements of the array $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, print "YES" if you can make array $$$a$$$ equal to array $$$b$$$ and "NO" otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Example
Input
7
3
1 2 3
1 2 3
4
1 4 5 2
1 5 4 3
1
9
8
6
6 7 6 7 6 7
7 6 7 6 7 6
9
9 8 7 6 5 4 3 2 1
9 9 8 2 4 4 3 5 3
3
1 1 2
2 1 1
2
1 2
1 1
Output
YES
YES
NO
YES
NO
YES
NO
Note

For the first test case, arrays $$$a$$$ and $$$b$$$ are already equal.

For the second test case, let us choose $$$l = 2$$$ and $$$r = 4$$$. Now, we update the array $$$a$$$ in the following manner:

  • For $$$i = 2$$$, we have $$$i - l = 2 - 2 = 0$$$, which is even. Hence, set $$$a_2 := a_2 + 1 = 4 + 1 = 5$$$.
  • For $$$i = 3$$$, we have $$$i - l = 3 - 2 = 1$$$, which is odd. Hence, set $$$a_3 := a_3 - 1 = 5 - 1 = 4$$$.
  • For $$$i = 4$$$, we have $$$i - l = 4 - 2 = 2$$$, which is even. Hence, set $$$a_4 := a_4 + 1 = 2 + 1 = 3$$$.

Finally, we have array $$$a = [1, 5, 4, 3]$$$ and array $$$b = [1, 5, 4, 3]$$$.

For the third test case, it can be shown that it is impossible to make array $$$a$$$ equal to array $$$b$$$.