## Valentine's Day '19 S5 - A Top Tree Problem

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Points: 25 (partial)
Time limit: 2.5s
Java 3.0s
Memory limit: 512M

Author:
Problem types
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Jonathan is making a connected tree of nodes, and bidirectional edges. He wants to give the tree to <REDACTED> for Valentine's Day. However, he wants to make sure the tree is good looking.

Jonathan defines a simple path in the tree as a path where every node is traversed at most once.

To determine whether the tree is good looking, he will give you queries that you must answer for him:

• v k u_1 u_2 ... u_k Is there a simple path that visits in that order, if at most bidirectional edges are added into the tree?

. is guaranteed to be distinct.

#### Input Specification

The first line will contain two integers, .

The next lines will each contain two integers , indicating that there is a bidirectional edge between and . It is guaranteed that the tree is connected.

The next lines will each contain a query as defined above.

#### Output Specification

For each query, output 1 if the answer to the query is yes, and 0 otherwise.

No further constraints.

#### Sample Input 1

5 3
1 2
2 3
2 4
1 5
0 3 5 2 3
0 3 3 4 5
0 3 1 3 2

#### Sample Output 1

1
0
0

#### Sample Input 2

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

#### Sample Output 2

1
0
1
1
0