Problem Statement

315-san is going to give a sequence to a close friend, Nekkoara-san, as a birthday present.
Nekkoara-san likes the sequence $B_i$ of length $N$, so 315-san prepared this sequence and headed for Nekkoara-san's house.
However, on checking the sequence while on the train, 315-san realized that a different sequence $A_i$ had been brought by mistake.
Fortunately, there are still $P$ minutes until arrival. Per $1$ minute, 315-san can perform either of the following operations only once.
Operation 1. Choose integers $i, j$ such that $1 \leq i, j \leq N$, and add $A_j$ to $A_i$.
Operation 2. Replace every element of the sequence with its remainder modulo $P$.
Now, can 315-san successfully give the sequence $B_i$?

Input

$N \ P$
$A_1 \ A_2 \ \cdots \ A_N$
$B_1 \ B_2 \ \cdots \ B_N$

• $1 \leq N \leq 10^5$
• $P = 223577$ (prime)
• $0 \leq A_i, B_i < P$
• All inputs are integers.

Output

If the sequence $B_i$ cannot be made in time, print -1.
Otherwise, first print the number of operations performed, $n$, on the $1$st line.
On each of the following $n$ lines, print $1 \ i \ j$ if operation $1$ was performed, or $2$ if operation $2$ was performed.
In either case, print a newline at the end.

Sample

2 223577
1 1
4 5

5
1 1 2
1 1 2
1 1 2
1 2 1
2

1 223577
101090
9

11
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
2

5 223577
1 2 3 4 5
1 3 6 10 15

10
1 5 4
1 5 3
1 5 2
1 5 1
1 4 3
1 4 2
1 4 1
1 3 2
1 3 1
1 2 1