To celebrate the start of spring, Farmer John's $N$ cows $(1≤N≤2⋅10^5)$ have invented an intriguing new dance, where they stand in a circle and re-order themselves in a predictable way.

Specifically, there are $N$ positions around the circle, numbered sequentially from $0$ to $N−1$, with position $0$ following position $N−1$. A cow resides at each position. The cows are also numbered sequentially from $0$ to $N−1$. Initially, cow $i$ starts in position $i$. You are told a set of $K$ positions $0\leq A_1<A_2....A_K<N$ that are "active", meaning the cows in these positions are the next to move (1≤K≤N).

In each minute of the dance, two things happen. First, the cows in the active positions rotate: the cow at position $A_1$ moves to position $A_2$, the cow at position $A_2$ moves to position $A_3$, and so on, with the cow at position $A_K$ moving to position $A_1$. All of these $K$ 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: $A_1$ becomes $A_1+1,A_2$ becomes $A_2+1$, and so on (if $A_i=N-1$ for some active position, then $A_i$ circles back around to 0).

Please calculate the order of the cows after $T$ minutes of the dance (1≤T≤10^9).

INPUT FORMAT (input arrives from the terminal / stdin):

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

OUTPUT FORMAT (print output to the terminal / stdout):

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

5 3 4
0 2 3

1 2 3 4 0

For the example above, here are the cow orders and $A$ for the first four timesteps:

Initial, T = 0: order = [0 1 2 3 4], A = [0 2 3]
T = 1: order = [3 1 0 2 4]
T = 1: A = [1 3 4]
T = 2: order = [3 4 0 1 2]
T = 2: A = [2 4 0]
T = 3: order = [2 4 3 1 0]
T = 3: A = [3 0 1]
T = 4: order = [1 2 3 4 0]

SCORING:

• Inputs 2-7: N≤1000,T≤10000
• Inputs 8-13: No additional constraints.