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.

• Split A off at the positions where two different elements are adjacent to each other.
• 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".
• Construct a sequence consisting of the integer pairs after the replacement without changing the order.

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

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.

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

见题面 Input 部分

见题面 Output 部分