A15336 | Madoka and Formal Statement

Given an array of integer $a_1, a_2, \ldots, a_n$ . In one operation you can make $a_i := a_i + 1$ if $i < n$ and $a_i \leq a_{i + 1}$ , or $i = n$ and $a_i \leq a_1$ .

You need to check whether the array $a_1, a_2, \ldots, a_n$ can become equal to the array $b_1, b_2, \ldots, b_n$ in some number of operations (possibly, zero). Two arrays $a$ and $b$ of length $n$ are called equal if $a_i = b_i$ for all integers $i$ from $1$ to $n$ .

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

The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) – the length of the array.

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

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

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

For each test case, output "YES" if you can get the array $b$ , otherwise output "NO".

You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).