Awkward operation

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Algorithms, Merge Sort, Sorting

Details

Problem

You are given two sequences $a$ and $b$ consisting of $n$ integers. You may choose any index $i$ $(1 < i < n)$ and simultanously apply the following changes :

$a_{i-1} := a_{i-1} +a_i$
$a_i := -a_i$
$a_{i+1} := a_{i+1} + a_i$

Determine whether you can make array $a$ equal to array $b$ after applying this operation any number of times (possibly zero).

Input

The first line contains one integer $t$ $(1 \leq t \leq 10^5)$ --- the number of test cases.

The first line of each test case contains a single integer $n$ $(1 \leq n \leq 3\cdot10^5)$ --- the number of integers in each sequence.

The second line of each test case contains $n$ integers $a_1,a_2,...,a_n$ $(-10^9 \leq a_i \leq 10^9)$ .

The third line of each test case contains $n$ integers $b_1,b_2,...,b_n$ $(-10^9 \leq b_i \leq 10^9)$ .

Output

For each test case, output "Yes" (without quotes) if $b$ can be obtained by applying the aforementioned operation on $a$ any number of times, and "No" (without quotes) otherwise.

Sample Input

5
3
5 -1 3
4 1 2
4
3 2 -2 -3
3 0 2 -5
7
-10 -3 3 -4 -1 7 2
-15 1 1 3 0 2 2
4
1 -1 1 -1
-1 1 -1 1
7
-10 -3 3 -4 -1 7 2
-15 1 1 3 0 4 -2

Sample Output

Yes
Yes
Yes
No
No

Time Limit: 2

Memory Limit: 256

Source Limit:

Explanation

In the first test case, we can obtain array $[5,-1,3]$ by applying the operation on index $i= 2$ .

In the first test case, we can obtain array $[3,0,2,-5]$ by applying the operation on index $i=3$ .

Contributers:

Nabil Boudraa

Divyam Agarwal