Rotate and Shift

문제

To celebrate the start of spring, Farmer John's $NN$ cows ($1\le N\le 2\cdot {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 2\; \backslash cdot\; 10^5$) have invented an intriguing new dance, where they stand in a circle and re-order themselves in a predictable way.

Specifically, there are $NN$ positions around the circle, numbered sequentially from $00$ to $N-1N-1$, with position $00$ following position $N-1N-1$. A cow resides at each position. The cows are also numbered sequentially from $00$ to $N-1N-1$. Initially, cow $ii$ starts in position $ii$. You are told a set of $KK$ positions that are "active", meaning the cows in these positions are the next to move ($1\le K\le N1\; \backslash leq\; K\; \backslash leq\; N$).

In each minute of the dance, two things happen. First, the cows in the active positions rotate: the cow at position $A_{1}A\_1$ moves to position $A_{2}A\_2$, the cow at position $A_{2}A\_2$ moves to position $A_{3}A\_3$, and so on, with the cow at position $A_{K}A\_K$ moving to position $A_{1}A\_1$. All of these $KK$ moves happen simultaneously, so the after the rotation is complete, all of the active positions still contain exactly one cow. Next, the active positions themselves shift: $A_{1}A\_1$ becomes $A_1+1A\_1+1$, $A_{2}A\_2$ becomes $A_2+1A\_2+1$, and so on (if $A_i=N-1A\_i\; =\; N-1$ for some active position, then $A_{i}A\_i$ circles back around to $00$).

Please calculate the order of the cows after $TT$ minutes of the dance ($1\le T\le {10}^{9}1\backslash le\; T\backslash le\; 10^9$).

입력

The first line contains three integers $NN$, $KK$, and $TT$.

The second line contains $KK$ integers representing the initial set of active positions $A_1,A_2,\dots A_{K}A\_1,A\_2,\; \backslash ldots\; A\_K$. Recall that $A_1=0A\_1\; =\; 0$ and that these are given in increasing order.

출력

Output the order of the cows after $TT$ minutes, starting with the cow in position $00$, separated by spaces.

5 3 4
0 2 3

1 2 3 4 0