Problem L

I love a game series called "Wario Land", so I'd like to make a very difficult (indeed!!!) problem about it :) A big thank you goes to Erjin Zhou, for the idea and reference code. And a small thank you goes to Wenbin Tang, for reminding me that "Rujia Liu" also contains the letter L!

Suppose there are n places in the very beginning of Wario Land. The land was almost deprecated, so it does not have any roads at all! You'll be given m operations. Execute them one by one, and output the results.

1 x y

Wario wants to build a direct road between place x and y. If x and y are already connected (directly or indirectly), ignore this command (because Wario thinks it's a waste of time!).

2 x v

Change place x's treasure value to v. This is due to newly discovered treasures, or treasures that are stolen by someone else.

3 x y v

Among the places along the path between x and y (including x and y), how many of them have treasure value <= v? Wario also needs the product of these treasure values, modulo k (see below).

Input

The input contains several test cases. In each test case, the first line contains three integers n, m, k(1<=n<=50,000, 1<=m<=100,000, 2<=k<=33333). Places are numbered from 1 to n. The second line contains n integers V[i] (1<=V[i]<=k), the initial treasure values of each place. Each of the next m lines contains an operation. For each operation, 1<=x,y<=n, 1<=v<=k. The input is terminated by end-of-file (EOF). The size of input file does not exceed 10MB.

Output

For each type-3 operation, output the number of places and the product of their treasure values, modulo k. If there is no path between x and y, or every place along the path has treasure value > v, output a single 0 (rather than 0 0 or 0 1).

Sample Input

4 8 39
2 3 4 5
1 1 2
3 2 3 5
1 1 3
3 2 3 5
1 1 4
3 3 4 4
3 3 4 5
3 3 4 1

Output for the Sample Input

0
3 24
2 8
3 1
0

Obfuscation

In order to prevent you from preprocessing the operations, we adopt the following obfuscation scheme:

Each type-1 operation becomes 1 x+d y+d

Each type-2 operation becomes 2 x+d v+d

Each type-3 operation becomes 3 x+d y+d v+d

Where d is the last integer that you output, before processing this operation. If you haven't output anything yet, d=0.

After the obfuscation, the sample input would be:

4 8 39
2 3 4 5
1 1 2
3 2 3 5
1 1 3
3 2 3 5
1 25 28
3 27 28 28
3 11 12 13
3 4 5 2

This is the real input that your program will read.