A long time ago, in the not-so-distant LCT (land of the carrot trees), where carrots grow on trees, lived a magical carrot. In this magical land, there were ~N~ cities numbered ~1, 2, \dots, N~, connected with ~N-1~ roads, with no cycles. Over the course of ~Q~ days, some interesting things happened to the roads:

• A x y z: A new road of durability ~z~ is built between cities ~x~ and ~y~
• R x y: The road between cities ~x~ and ~y~ is destroyed by a rampaging rabbit (it is guaranteed to exist prior to the operation)
• Q x y: The eccentric king demanded to know the ~XOR~ of the durability of all roads on the path between cities ~x~ and ~y~

It is guaranteed that there will be at most one path between any two cities at any point in time.

Can you help the people of LCT by implementing a program to simulate these events?

Constraints

For all subtasks:

The durability of a path will be a positive integer in the range ~[1, 10^6]~.

Subtask 1 [20%]

~1 \le N \le 1\,000~

~1 \le Q \le 1\,000~

Subtask 2 [80%]

~1 \le N \le 10^5~

~1 \le Q \le 10^5~

Input Specification

The first line of input will have two integers, ~N~ and ~Q~.
The next ~N - 1~ lines will contain three integers, ~a_i, b_i, c_i~, indicating there is a road of durability ~c_i~ between cities ~a_i~ and ~b_i~.
The next ~Q~ lines will each contain a valid query.

Output Specification

For each Q query, print the answer to it on a new line. If the two cities are not connected, output -1.

Sample Input 1

5 4
1 2 3
2 4 5
3 5 6
2 3 8
R 3 2
A 3 1 6
Q 5 4
Q 3 2

Sample Output 1

6
5

Sample Input 2

6 8
1 2 3
3 4 5
4 5 6
4 1 8
6 1 4
Q 6 5
Q 3 2
R 4 3
R 4 1
A 1 3 8
Q 3 2
Q 4 5
Q 6 1

Sample Output 2

10
14
11
6
4