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문제

There are $N$ balls on the number line, each of diameter $1$, numbered from $1$ through $N$. Ball $i$'s leftmost point is located at position $p_i$. Additionally, there is an immovable wall located at position $P$. You have to process $Q$ queries of one of the following forms:

  • "1 $x$": Insert a new ball with its leftmost point at $x$. If this spot is already occupied, do nothing.
  • "2": Roll the leftmost ball to the right. When a rolling ball (possibly after moving distance zero) collides with a stationary ball, it stops, and the stationary ball begins rolling in the same direction. Specifically, a rolling ball stops at the position $1$ less than the position of the object it collided with. A ball stops when it reaches the wall.

Calculate the final positions of the balls.

입력

The first line contains three integers $N$, $Q$, and $P$: the initial number of balls, the number of queries, and the position of the wall ($1 \leq N, Q \leq 10^5$, $N \leq P \leq 10^9$).

The second line contains $N$ integers $p_1, p_2, \ldots, p_N$ ($0 \leq p_i < P$). It is guaranteed the positions are distinct.

The next $Q$ lines describe the queries and may have one of the following forms:

  • "1 $x$" ($0 \leq x < P$)
  • "2"

출력

Print out the final positions of the balls in increasing order on a single line, separated by spaces.

예제 입력 1

2 1 5
1 3
2

예제 출력 1

2 4

예제 입력 2

5 3 10
1 8 3 7 2
2
1 4
2

예제 출력 2

1 3 5 6 8 9