[Solution] Array Decrements Codeforces Solution

[Solution] Array Decrements Codeforces Solution

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

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

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

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

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

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

Input

The first line of the input contains an integer t$t$ (1≤t≤104$1\le t\le {10}^4$) —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$n$ (1≤n≤5⋅104$1\le n\le 5\cdot {10}^4$).

Array Decrements Codeforces Solution

The second line of each test case contains exactly n$n$ non-negative integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (0≤ai≤109$0\le a_i\le {10}^9$).

The third line of each test case contains exactly n$n$ non-negative integers b1,b2,…,bn$b_1,b_2,\dots ,b_n$ (0≤bi≤109$0\le b_i\le {10}^9$).

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

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$b$ from an array a$a$;
• 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).