Problem Statement

You are given positive integers N, M, K, and a sequence of positive integers of length $N, (C_1, C_2, \ldots, C_N)$. For each $r = 0, 1, 2, \ldots, N-1$, print the answer to the following problem.

There is a sequence of N colored balls. For $i = 1, 2, \ldots, N$, the color of the i-th ball from the beginning of the sequence is C_i.
Additionally, there are M empty boxes numbered 1 to M.
Determine the total number of balls in the boxes after performing the following steps.

• First, perform the following operation r times.

• Move the frontmost ball in the sequence to the end of the sequence.

• Then, repeat the following operation as long as at least one ball remains in the sequence.

• If there is a box that already contains at least one but fewer than K balls of the same color as the frontmost ball in the sequence, put the frontmost ball into that box.

• If there is no such box,
• If there is an empty box, put the frontmost ball into the one with the smallest box number.
• If there are no empty boxes, eat the frontmost ball without putting it into any box.

Input

The input is given from Standard Input in the following format:
N M K
$C_1 C_2 \ldots C_N$

Output

Print the answer X_r to the problem for each $r = 0, 1, 2, \ldots, N-1 over N$ lines as follows:
X_0
X_1
$\vdots$
X_{N-1}

Constraints

• All input values are integers.
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M, K \leq N$
• $1 \leq C_i \leq N$

Sample Input 1

7 2 2
1 2 3 5 2 5 4

Sample Output 1

3
3
3
4
4
3
2

For example, let us explain the procedure for r = 1.
First, perform the operation "Move the frontmost ball in the sequence to the end of the sequence" once, and the sequence of ball colors becomes (2, 3, 5, 2, 5, 4, 1).
Then, proceed with the operation of putting balls into boxes as follows:

• First operation: The color of the frontmost ball is 2. There is no box with at least one but fewer than two balls of color 2, so put the frontmost ball into the empty box with the smallest box number, box 1.
• Second operation: The color of the frontmost ball is 3. There is no box with at least one but fewer than two balls of color 3, so put the frontmost ball into the empty box with the smallest box number, box 2.
• Third operation: The color of the frontmost ball is 5. There is no box with at least one but fewer than two balls of color 5 and no empty boxes, so eat the frontmost ball.
• Fourth operation: The color of the frontmost ball is 2. There is a box, box 1, with at least one but fewer than two balls of color 2, so put the frontmost ball into box 1.
• Fifth operation: The color of the frontmost ball is 5. There is no box with at least one but fewer than two balls of color 5 and no empty boxes, so eat the frontmost ball.
• Sixth operation: The color of the frontmost ball is 4. There is no box with at least one but fewer than two balls of color 4 and no empty boxes, so eat the frontmost ball.
• Seventh operation: The color of the frontmost ball is 1. There is no box with at least one but fewer than two balls of color 1 and no empty boxes, so eat the frontmost ball.

The final total number of balls in the boxes is 3, so the answer to the problem for r = 1 is 3.

Sample Input 2

20 5 4
20 2 20 2 7 3 11 20 3 8 7 9 1 11 8 20 2 18 11 18

Sample Output 2

14
14
14
14
13
13
13
11
8
9
9
11
13
14
14
14
14
14
14
13

见题面 Input 部分

见题面 Output 部分