Codeforces Round 746 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

bitmasks

constructive algorithms

dfs and similar

dp

graphs

trees

*1700

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Bakry and Partitioning

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBakry faced a problem, but since he's lazy to solve it, he asks for your help.

You are given a tree of $$$n$$$ nodes, the $$$i$$$-th node has value $$$a_i$$$ assigned to it for each $$$i$$$ from $$$1$$$ to $$$n$$$. As a reminder, a tree on $$$n$$$ nodes is a connected graph with $$$n-1$$$ edges.

You want to delete at least $$$1$$$, but at most $$$k-1$$$ edges from the tree, so that the following condition would hold:

For every connected component calculate the bitwise XOR of the values of the nodes in it. Then, these values have to be the same for all connected components.

Is it possible to achieve this condition?

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ $$$(1 \leq t \leq 5 \cdot 10^4)$$$. Description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ $$$(2 \leq k \leq n \leq 10^5)$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, ..., a_n$$$ $$$(1 \leq a_i \leq 10^9)$$$.

The $$$i$$$-th of the next $$$n-1$$$ lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \leq u_i, v_i \leq n$$$, $$$u_i\neq v_i$$$), which means that there's an edge between nodes $$$u_i$$$ and $$$v_i$$$.

It is guaranteed that the given graph is a tree.

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

Output

For each test case, you should output a single string. If you can delete the edges according to the conditions written above, output "YES" (without quotes). Otherwise, output "NO" (without quotes).

You can print each letter of "YES" and "NO" in any case (upper or lower).

Example

Input

5 2 2 1 3 1 2 5 5 3 3 3 3 3 1 2 2 3 1 4 4 5 5 2 1 7 2 3 5 1 2 2 3 1 4 4 5 5 3 1 6 4 1 2 1 2 2 3 1 4 4 5 3 3 1 7 4 1 2 2 3

Output

NO YES NO YES NO

Note

It can be shown that the objection is not achievable for first, third, and fifth test cases.

In the second test case, you can just remove all the edges. There will be $$$5$$$ connected components, each containing only one node with value $$$3$$$, so the bitwise XORs will be $$$3$$$ for all of them.

In the fourth test case, this is the tree: .

You can remove an edge $$$(4,5)$$$

The bitwise XOR of the first component will be, $$$a_1 \oplus a_2 \oplus a_3 \oplus a_4 = 1 \oplus 6 \oplus 4 \oplus 1 = 2$$$ (where $$$\oplus$$$ denotes the bitwise XOR).

The bitwise XOR of the second component will be, $$$a_5 = 2$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/09/2024 09:45:53 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|