Uncle Bogdan and Country Happiness

Description:

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10000$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^5$$$; $$$0 \le m \le 10^9$$$) — the number of cities and citizens.

The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_{n}$$$ ($$$0 \le p_i \le m$$$; $$$p_1 + p_2 + \ldots + p_{n} = m$$$), where $$$p_i$$$ is the number of people living in the $$$i$$$-th city.

The third line contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_{n}$$$ ($$$-10^9 \le h_i \le 10^9$$$), where $$$h_i$$$ is the calculated happiness index of the $$$i$$$-th city.

Next $$$n − 1$$$ lines contain description of the roads, one per line. Each line contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le n$$$; $$$x_i \neq y_i$$$), where $$$x_i$$$ and $$$y_i$$$ are cities connected by the $$$i$$$-th road.

It's guaranteed that the sum of $$$n$$$ from all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, print YES, if the collected data is correct, or NO — otherwise. You can print characters in YES or NO in any case.

Sample Input:

2
7 4
1 0 1 1 0 1 0
4 0 0 -1 0 -1 0
1 2
1 3
1 4
3 5
3 6
3 7
5 11
1 2 5 2 1
-11 -2 -6 -2 -1
1 2
1 3
1 4
3 5

Sample Output:

YES
YES

Sample Input:

2
4 4
1 1 1 1
4 1 -3 -1
1 2
1 3
1 4
3 13
3 3 7
13 1 4
1 2
1 3

Sample Output:

NO
NO

Note:

Let's look at the first test case of the first sample:

At first, all citizens are in the capital. Let's describe one of possible scenarios:

• a person from city $$$1$$$: he lives in the capital and is in good mood;
• a person from city $$$4$$$: he visited cities $$$1$$$ and $$$4$$$, his mood was ruined between cities $$$1$$$ and $$$4$$$;
• a person from city $$$3$$$: he visited cities $$$1$$$ and $$$3$$$ in good mood;
• a person from city $$$6$$$: he visited cities $$$1$$$, $$$3$$$ and $$$6$$$, his mood was ruined between cities $$$1$$$ and $$$3$$$;

In total,

• $$$h_1 = 4 - 0 = 4$$$,
• $$$h_2 = 0$$$,
• $$$h_3 = 1 - 1 = 0$$$,
• $$$h_4 = 0 - 1 = -1$$$,
• $$$h_5 = 0$$$,
• $$$h_6 = 0 - 1 = -1$$$,
• $$$h_7 = 0$$$.

The second case of the first test:

All people have already started in bad mood in the capital — this is the only possible scenario.

The first case of the second test:

The second case of the second test:

It can be proven that there is no way to achieve given happiness indexes in both cases of the second test.