Rotate and Shift

To celebrate the start of spring, Farmer John's $N$ cows ($1 \leq N \leq 2 \cdot 10^5$) have invented a new dance. The cows stand in a circle and reorder themselves in a predictable way.

There are $N$ positions around the circle, numbered from $0$ to $N-1$, with position $0$ following position $N-1$. Each position holds one cow, and the cows are also numbered from $0$ to $N-1$. Initially, cow $i$ is in position $i$. A set of $K$ positions $0=A_1<A_2<\ldots<A_K<N$ is marked as active ($1 \leq K \leq N$). The cows in the active positions move next.

Each minute, two things happen. First, the cows in the active positions rotate: the cow at $A_1$ moves to $A_2$, the cow at $A_2$ moves to $A_3$, and so on, and the cow at $A_K$ moves to $A_1$. All $K$ moves happen at the same time, so every active position still holds exactly one cow afterward. Second, the active positions shift: $A_1$ becomes $A_1+1$, $A_2$ becomes $A_2+1$, and so on. If an active position is $N-1$, it wraps around to $0$.

The first line contains three integers $N$, $K$, and $T$.

The second line contains $K$ integers $A_1, A_2, \ldots, A_K$, the initial set of active positions. Recall that $A_1 = 0$ and that these are given in increasing order.

Output the order of the cows after $T$ minutes, starting with the cow in position $0$, separated by spaces.