## Inaho VIII

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Points: 20
Time limit: 3.0s
Memory limit: 512M

Author:
Problem types

Inaho was thinking of a tree problem, when he came up with this rather beautiful problem!

Given a tree originally rooted at containing nodes each with a value and an arbitrary value , support of following operations:

• 1 R Reroot the tree so that node is the root.
• 2 a b Print the highest common ancestor of nodes and .
• 3 a b Print the sum of all nodes' on the path from to , inclusive.
• 4 a b Print the product of all nodes' on the path from to , inclusive, modulo .
• 5 a b Print the minimum of all nodes' on the path from to , inclusive.
• 6 a b Print the maximum of all nodes' on the path from to , inclusive.
• 7 a b Print the greatest common divisor of all nodes' on the path from to , inclusive.
• 8 a b Print the bitwise AND of all nodes' on the path from to , inclusive.
• 9 a b Print the bitwise OR of all nodes' on the path from to , inclusive.
• 10 a b Print the bitwise XOR of all nodes' on the path from to , inclusive.
• 11 a b Print the number of nodes whose on the path from to , inclusive.
• 12 a b Print the number of nodes whose on the path from to , inclusive.
• 13 a b Print the value that minimizes , and of all nodes on the path from to , inclusive. Print if there is no such node where .
• 14 a b Print the value that minimizes , and of all nodes on the path from to , inclusive. Print if there is no such node where .

It is guaranteed .

#### Input Specification

The first line will contain three space-separated integers, , the number of nodes, the number of operations, and the arbitrary value , respectively.

The second line will contain space-separated integers, , the values of each node.

The next lines will each contain two space-separated integers, , indicating that nodes and are connected by an edge. It is guaranteed the entire tree is connected.

The next lines will each contain a valid operation as defined above.

#### Output Specification

For each operation that requires something to be outputted (everything except operation ), print the answer on its own line.

#### Sample Input

6 15 3
4 10 2 2 5 1
1 2
1 3
3 4
3 5
3 6
2 1 2
1 3
2 1 2
3 2 5
4 4 1
5 1 6
6 3 5
7 2 3
8 3 4
9 5 3
10 6 2
11 2 6
12 3 1
13 4 5
14 1 2

#### Sample Output

1
3
21
16
1
5
2
2
7
13
2
1
5
3