B. Array Decrements
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Kristina has two arrays $$$a$$$ and $$$b$$$, each containing $$$n$$$ non-negative integers. She can perform the following operation on array $$$a$$$ any number of times:

  • apply a decrement to each non-zero element of the array, that is, replace the value of each element $$$a_i$$$ such that $$$a_i > 0$$$ with the value $$$a_i - 1$$$ ($$$1 \le i \le n$$$). If $$$a_i$$$ was $$$0$$$, its value does not change.

Determine whether Kristina can get an array $$$b$$$ from an array $$$a$$$ in some number of operations (probably zero). In other words, can she make $$$a_i = b_i$$$ after some number of operations for each $$$1 \le i \le n$$$?

For example, let $$$n = 4$$$, $$$a = [3, 5, 4, 1]$$$ and $$$b = [1, 3, 2, 0]$$$. In this case, she can apply the operation twice:

  • after the first application of the operation she gets $$$a = [2, 4, 3, 0]$$$;
  • after the second use of the operation she gets $$$a = [1, 3, 2, 0]$$$.

Thus, in two operations, she can get an array $$$b$$$ from an array $$$a$$$.

Input

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) —the number of test cases in the test.

The descriptions of the test cases follow.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 5 \cdot 10^4$$$).

The second line of each test case contains exactly $$$n$$$ non-negative integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^9$$$).

The third line of each test case contains exactly $$$n$$$ non-negative integers $$$b_1, b_2, \dots, b_n$$$ ($$$0 \le b_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ values over all test cases in the test does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output on a separate line:

  • YES, if by doing some number of operations it is possible to get an array $$$b$$$ from an array $$$a$$$;
  • NO otherwise.

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

Example
Input
6
4
3 5 4 1
1 3 2 0
3
1 2 1
0 1 0
4
5 3 7 2
1 1 1 1
5
1 2 3 4 5
1 2 3 4 6
1
8
0
1
4
6
Output
YES
YES
NO
NO
YES
NO
Note

The first test case is analyzed in the statement.

In the second test case, it is enough to apply the operation to array $$$a$$$ once.

In the third test case, it is impossible to get array $$$b$$$ from array $$$a$$$.