A new school year has started. The high school for gifted
students of Ho Chi Minh city has $N$ classes numbered from $1$ to $N$. All $N$ classes will go through
$M$ studying weeks. The
high school has $N$
teachers numbered from $1$
to $N$. At the beginning
teacher $i$ is assigned to
class $i$.
In order to improve the students adaptability to new
knowledge or new teaching methods, the principal has plans to
reassign the teachers every few weeks. A
reassignment only happens at the beginning of a week (on
Monday before classes start) and a week has
at most $1$
reassignment. A reassignment is to rotate $K$ teachers $p_1, p_2, p_3, \ldots , p_ K$,
described as follows:
After the reassignment, the teachers will stay at the newly
assigned classrom, until he is reassigned again.
The principal continuously add shuffle plans and he also
asks questions: “When all the previous reassignment plans comes
to effect, which class will teacher $d$ teach on Tuesday of the
$x$th week?” Your task is
to help him answer all those questions.
Input
The first line contains $3$ integers: $N$, $M$ and $Q$  the number of queries
($1 \leq N,M,Q \leq
10^5$). The next $Q$ lines describes $Q$ queries, each will be in either of
the $2$ forms:

$0$ $K$ $x$ $p_1$ $p_2$ …$p_ K$  add a plan to rotate
$K$ teachers
$p_1, p_2, \ldots p_
K$ on Monday of the $x$th week ($1 \leq x \leq M$, $2 \leq K \leq 10$, all
$K$ values in
$p$ are unique).

$1$ $d$ $x$  ask which class is taught by
teacher $d$ on Tuesday
of the $x$th
week.
It is guaranteed that there are no two queries of type
$0$ has the same value
$x$.
Output
For each of the queries type $1$, print the answer in a single
line.
Clarification for the second sample
Initial assignment:

Class $1$

Class $2$

Class $3$

Week $1$

$1$

$2$

$3$

Week $2$

$1$

$2$

$3$

Week $3$

$1$

$2$

$3$

Week $4$

$1$

$2$

$3$

After rotate $(3, 2)$
on Monday of the $2^\textrm
{nd}$ week:

Class $1$

Class $2$

Class $3$

Week $1$

$1$

$2$

$3$

Week $2$

$1$

$3$

$2$

Week $3$

$1$

$3$

$2$

Week $4$

$1$

$3$

$2$

After rotate $(3,1,2)$
on Monday of the $3^\textrm
{rd}$ week:

Class $1$

Class $2$

Class $3$

Week $1$

$1$

$2$

$3$

Week $2$

$1$

$3$

$2$

Week $3$

$3$

$2$

$1$

Week $4$

$3$

$2$

$1$

Sample Input 1 
Sample Output 1 
3 4 5
1 3 4
0 2 2 3 2
1 3 2
1 2 4
1 1 4

3
2
3
1

Sample Input 2 
Sample Output 2 
3 4 6
1 3 4
0 2 2 3 2
1 3 2
0 3 3 3 1 2
1 2 4
1 1 4

3
2
2
3
