Figure Fixing

Description:

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".

Sample Input:

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

Sample Output:

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.