Card Rearrangement

There are $2n$ cards numbered from $1$ to $2n$, stacked so that from top to bottom they are in the order $1, 2, 3, \dots, 2n$.

This stack is rearranged by applying the following two operations some number of times.

Cut by an integer $k$

Take the top $k$ cards as pile $A$ and leave the remaining cards as pile $B$, then place pile $B$ on top of pile $A$. In other words, after the cut the cards of pile $B$ are on top, with the cards of pile $A$ below them.

Riffle shuffle

Split the top $n$ cards into pile $A$ and the remaining $n$ cards into pile $B$, then merge them into a single stack so that from the top the order is the $1$st card of $A$, the $1$st card of $B$, the $2$nd card of $A$, the $2$nd card of $B$, $\dots$, the $n$th card of $A$, the $n$th card of $B$.

Following the given instructions, rearrange all the cards and then print the card numbers from top to bottom.

• The first line contains $n$ ($1 \le n \le 100$); that is, there are $2n$ cards.
• The second line contains the number of operations $m$ ($1 \le m \le 1000$).
• Each of the next $m$ lines (lines $3$ through $m+2$) contains a single integer $k$ with $0 \le k \le 2n-1$, specifying the rearrangement operations in order.
  • If $k = 0$, perform a riffle shuffle.
  • If $1 \le k \le 2n-1$, perform a cut by $k$.

Print $2n$ lines. The first line contains the number of the topmost card after all rearrangements are finished, the second line contains the number of the second card from the top, and in general the $i$-th line contains the number of the $i$-th card from the top.