Figure Fixing
Description
You have a connected undirected graph made of $n$ nodes and $m$ edges. The $i$-th node has a value $v_i$ and a target value $t_i$.
In an operation, you can choose an edge $(i, j)$ and add $k$ to both $v_i$ and $v_j$, where $k$ can be any integer. In particular, $k$ can be negative.
Your task to determine if it is possible that by doing some finite number of operations (possibly zero), you can achieve for every node $i$, $v_i = t_i$.
The first line contains a single integer $t$ ($1 \leq t \leq 1000$), the number of test cases. Then the test cases follow.
The first line of each test case contains two integers $n$, $m$ ($2 \leq n \leq 2\cdot 10^5$, $n-1\leq m\leq \min(2\cdot 10^5, \frac{n(n-1)}{2})$) — the number of nodes and edges respectively.
The second line contains $n$ integers $v_1\ldots, v_n$ ($-10^9 \leq v_i \leq 10^9$) — initial values of nodes.
The third line contains $n$ integers $t_1\ldots, t_n$ ($-10^9 \leq t_i \leq 10^9$) — target values of nodes.
Each of the next $m$ lines contains two integers $i$ and $j$ representing an edge between node $i$ and node $j$ ($1 \leq i, j \leq n$, $i\ne j$).
It is guaranteed that the graph is connected and there is at most one edge between the same pair of nodes.
It is guaranteed that the sum of $n$ over all testcases does not exceed $2 \cdot 10^5$ and the sum of $m$ over all testcases does not exceed $2 \cdot 10^5$.
For each test case, if it is possible for every node to reach its target after some number of operations, print "YES". Otherwise, print "NO".
Input
The first line contains a single integer $t$ ($1 \leq t \leq 1000$), the number of test cases. Then the test cases follow.
The first line of each test case contains two integers $n$, $m$ ($2 \leq n \leq 2\cdot 10^5$, $n-1\leq m\leq \min(2\cdot 10^5, \frac{n(n-1)}{2})$) — the number of nodes and edges respectively.
The second line contains $n$ integers $v_1\ldots, v_n$ ($-10^9 \leq v_i \leq 10^9$) — initial values of nodes.
The third line contains $n$ integers $t_1\ldots, t_n$ ($-10^9 \leq t_i \leq 10^9$) — target values of nodes.
Each of the next $m$ lines contains two integers $i$ and $j$ representing an edge between node $i$ and node $j$ ($1 \leq i, j \leq n$, $i\ne j$).
It is guaranteed that the graph is connected and there is at most one edge between the same pair of nodes.
It is guaranteed that the sum of $n$ over all testcases does not exceed $2 \cdot 10^5$ and the sum of $m$ over all testcases does not exceed $2 \cdot 10^5$.
Output
For each test case, if it is possible for every node to reach its target after some number of operations, print "YES". Otherwise, print "NO".
Samples
2
4 4
5 1 2 -3
3 3 10 1
1 2
1 4
3 2
3 4
4 4
5 8 6 6
-3 1 15 4
1 2
1 4
3 2
3 4
YES
NO
Note
Here is a visualization of the first test case (the orange values denote the initial values and the blue ones the desired values):
One possible order of operations to obtain the desired values for each node is the following:
- Operation $1$: Add $2$ to nodes $2$ and $3$.
- Operation $2$: Add $-2$ to nodes $1$ and $4$.
- Operation $3$: Add $6$ to nodes $3$ and $4$.
Now we can see that in total we added $-2$ to node $1$, $2$ to node $2$, $8$ to node $3$ and $4$ to node $4$ which brings each node exactly to it's desired value.
For the graph from the second test case it's impossible to get the target values.