Pride of Sniper

I should do my best to live up to Hifumi-chan's expectations. ...Let's go over the situation.

• The $x$-axis is the line connecting coconut $1$ and coconut $\frac{N}{2} + 1$.
• The $y$-axis is perpendicular to the $x$-axis and passes through my firing position, the center of the circle.

Since the coconuts are evenly spaced around the circle, for any coconut there is always exactly one other coconut at its reflection across the $x$-axis or the $y$-axis.

Subqueries

Sensei's program contains $M$ subqueries, numbered from $1$ to $M$. Each subquery is a command that changes the currently selected coconut. It has one of the following four forms.

• 1 a: Select the coconut $a$ steps counterclockwise from the currently selected coconut.
• 2 a: Select the coconut $a$ steps clockwise from the currently selected coconut.
• 3: Select the coconut at the reflection of the current coconut across the $x$-axis.
• 4: Select the coconut at the reflection of the current coconut across the $y$-axis.

Movement wraps around the circle: moving $1$ step counterclockwise goes from coconut $N$ to coconut $1$, or otherwise from coconut $i$ to coconut $i+1$. Likewise, moving $1$ step clockwise goes from coconut $1$ to coconut $N$, or otherwise from coconut $i$ to coconut $i-1$.

...But Sensei isn't going to execute just one subquery at a time.

Queries

The program also has $Q$ queries that either execute some of these $M$ subqueries or change their contents. Each query is one of the following two types.

• 1 i j: Execute all subqueries from subquery $i$ through subquery $j$, in increasing order of their numbers.

• 2 i j q or 2 i j q a: Replace every subquery from subquery $i$ through subquery $j$ with the same subquery.

  • $q = 1$: Given in the form 2 i j q a; change every subquery in the range to 1 a.
  • $q = 2$: Given in the form 2 i j q a; change every subquery in the range to 2 a.
  • $q = 3$: Given in the form 2 i j q; change every subquery in the range to 3.
  • $q = 4$: Given in the form 2 i j q; change every subquery in the range to 4.

Apparently coconut $S$ is selected initially. Starting from that state, the $Q$ queries will be processed in order. Whenever a 1 i j query finishes, Sensei will call out the number of the coconut selected at that moment.

After each 1 i j query, the next query starts with the newly selected coconut still selected.

Objective

All right. I understand. In the end, there's only one thing I want to know.

“Which coconut numbers will Sensei call out, and in what order?”

Knowing those numbers in advance should give me an advantage. Let's find them in order by following all the given queries.

Lines 2 through $M+1$ contain subqueries $1$ through $M$ in order, one per line. Each line has one of the following two forms.

• t a $(1 \le t \le 2$; $1 \le a \le N-1)$
• t $(3 \le t \le 4)$

Then lines $M+2$ through $M+Q+1$ contain the queries in execution order, one per line. Each line has one of the following three forms. $(1 \le i \le j \le M$; $1 \le q \le 4$; $1 \le a \le N-1)$

• 1 i j
• 2 i j q
• 2 i j q a

There is at least one query of type $1$.

Time limit

2000 ms

Memory limit

1024 MB

Checker

CUSTOM