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
```

## Comments