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Ex - Fill Triangle /

Time Limit: 4 sec / Memory Limit: 1024 MB

### 問題文

ブロックが三角形状に N 段並んでいます。上から i 段目には i 個のブロックが並んでいます。

6 以下の非負整数からなる列 A = (A_1, A_2, ..., A_N) を連長圧縮した列 P = ((a_1, c_1), (a_2, c_2), ..., (a_M, c_M)) が与えられます。

• 例えば A = (2, 2, 2, 5, 5, 1) のとき P = ((2, 3), (5, 2), (1, 1)) になります。

• すべての 1 \leq i \leq N を満たす整数 i について B_{N,i} = A_{i}
• すべての 1 \leq j \leq i \leq N-1 を満たす整数の組 i,j について B_{i,j}= (B_{i+1,j}+B_{i+1,j+1})\bmod 7

1. A を異なる要素が隣り合っている部分で分割する。
2. 分割した各数列 B に対して、B を 「B を構成する数」 と 「B の長さ」 からなる整数の組に置き換える。
3. 置き換えた整数の組を元の順番を保ったまま並べて列にする。

### 制約

• 1 \leq N \leq 10^9
• 1 \leq M \leq \min(N, 200)
• 1 \leq K \leq \min(N,5 \times 10^5)
• 0 \leq a_i \leq 6
• 1 \leq c_i \leq N
• \sum_{i=1}^M c_i = N
• 入力される値はすべて整数

### 入力

N M K
a_1 c_1
a_2 c_2
\vdots
a_M c_M


### 出力

B_{K,1} B_{K,2} \dots B_{K,K}


### 入力例 1

6 3 4
2 3
5 2
1 1


### 出力例 1

1 4 3 2


A = (2,2,2,5,5,1) です。また、ブロックに書かれる数は次のようになります。

     3
5 5
5 0 5
1 4 3 2
4 4 0 3 6
2 2 2 5 5 1


### 入力例 2

1 1 1
6 1


### 出力例 2

6


### 入力例 3

111111111 9 9
0 1
1 10
2 100
3 1000
4 10000
5 100000
6 1000000
0 10000000
1 100000000


### 出力例 3

1 0 4 2 5 5 5 6 3


Score : 600 points

### Problem Statement

Blocks are stacked in a triangle. The i-th column from the top has i blocks.

You are given a sequence P = ((a_1, c_1), (a_2, c_2), ..., (a_M, c_M)) which is a result of the run-length compression of a sequence A = (A_1, A_2, ..., A_N) consisting of non-negative integers less than or equal to 6.

• For example, when A = (2, 2, 2, 5, 5, 1), you are given P = ((2, 3), (5, 2), (1, 1)).

You will write a number on each block so that the following conditions are satisfied, where B_{i,j} denotes the number to write on the j-th block from the left in the i-th column from the top:

• For all integers i such that 1 \leq i \leq N, it holds that B_{N,i} = A_{i}.
• For all pairs of integers (i, j) such that 1 \leq j \leq i \leq N-1, it holds that B_{i,j}= (B_{i+1,j}+B_{i+1,j+1})\bmod 7.

Enumerate the numbers written on the blocks in the K-th column from the top.

What is run-length compression? The run-length compression is a conversion from a given sequence A to a sequence of pairs of integers obtained by the following procedure.
1. Split A off at the positions where two different elements are adjacent to each other.
2. For each subsequence B that has been split off, replace B with a integer pair of "the number which B consists of" and "the length of B".
3. Construct a sequence consisting of the integer pairs after the replacement without changing the order.

### Constraints

• 1 \leq N \leq 10^9
• 1 \leq M \leq \min(N, 200)
• 1 \leq K \leq \min(N,5 \times 10^5)
• 0 \leq a_i \leq 6
• 1 \leq c_i \leq N
• \sum_{i=1}^M c_i = N
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N M K
a_1 c_1
a_2 c_2
\vdots
a_M c_M


### Output

Print the answer in the following format. It is guaranteed that the answer is unique under the Constraint of the problem.

B_{K,1} B_{K,2} \dots B_{K,K}


### Sample Input 1

6 3 4
2 3
5 2
1 1


### Sample Output 1

1 4 3 2


We have A = (2,2,2,5,5,1). The number written on the blocks are as follows.

     3
5 5
5 0 5
1 4 3 2
4 4 0 3 6
2 2 2 5 5 1


### Sample Input 2

1 1 1
6 1


### Sample Output 2

6


### Sample Input 3

111111111 9 9
0 1
1 10
2 100
3 1000
4 10000
5 100000
6 1000000
0 10000000
1 100000000


### Sample Output 3

1 0 4 2 5 5 5 6 3