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 $$$a_i \gt 0$$$ 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).

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 $$$a$$$.

Array Decrements

Examples