[Solution] Madoka and Formal Statement Codeforces Solution

C. Madoka and Formal Statement

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Given an array of integer 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$. In one operation you can make 𝑎𝑖:=𝑎𝑖+1$a_i:=a_i+1$ if 𝑖<𝑛$i<n$ and 𝑎𝑖≤𝑎𝑖+1$a_i\le a_{i+1}$, or 𝑖=𝑛$i=n$ and 𝑎𝑖≤𝑎1$a_i\le a_1$.

You need to check whether the array 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ can become equal to the array 𝑏1,𝑏2,…,𝑏𝑛$b_1,b_2,\dots ,b_n$ in some number of operations (possibly, zero). Two arrays 𝑎$a$ and 𝑏$b$ of length 𝑛$n$ are called equal if 𝑎𝑖=𝑏𝑖$a_i=b_i$ for all integers 𝑖$i$ from 1$1$ to 𝑛$n$.

Input

The input consists of multiple test cases. The first line contains a single integer 𝑡$t$ (1≤𝑡≤4⋅104$1\le t\le 4\cdot {10}^4$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer 𝑛$n$ (2≤𝑛≤2⋅105$2\le n\le 2\cdot {10}^5$) – the length of the array.

The second line of each test case contains 𝑛$n$ integers 𝑎1,…,𝑎𝑛$a_1,\dots ,a_n$ (1≤𝑎𝑖≤109$1\le a_i\le {10}^9$) – the elements of the array 𝑎$a$.

The third line of each test case contains 𝑛$n$ integers 𝑏1,…,𝑏𝑛$b_1,\dots ,b_n$ (1≤𝑏𝑖≤109$1\le b_i\le {10}^9$) – the elements of the array 𝑏$b$.

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It is guaranteed that the sum of 𝑛$n$ over all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Output

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

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

Note

In the first test case, the array 𝑎$a$ is already equal to the array 𝑏$b$.

In the second test case, we can't get the array 𝑏$b$, because to do this we need to decrease 𝑎1$a_1$.

In the fifth test case, we can apply operations in order to the elements with indices 4,3,3,2,2,2,1,1,1,1$4,3,3,2,2,2,1,1,1,1$, and then get the array [5,5,5,5,5]$[5,5,5,5,5]$. After that, you can apply operations in order to elements with indices 5,4,4,3,1$5,4,4,3,1$ and already get an array [6,5,6,7,6]$[6,5,6,7,6]$.