One-Dimensional Cellular Automaton
One-Dimensional Cellular Automaton
There is a one-dimensional cellular automaton consisting of N cells. Cells are numbered from 0 to N-1.
Each cell has a state represented as a non-negative integer less than M. The states of cells evolve through discrete time steps. We denote the state of the i-th cell at time t as S(i, t). The state at time t+1 is de ned by the equation
S(i, t+1) = (A × S(i-1, t) + B × S(i, t) + C × S(i+1, t))mod M, (1)
where A, B and C are non-negative integer constants. For i < 0 or N ≤ i, we de ne S(i, t) = 0.
Given an automaton de nition and initial states of cells, your mission is to write a program that computes the states of the cells at a speci ed time T.
Входные данные
The input is a sequence of datasets. Each dataset is formatted as follows.
N M A B C T
S(0, 0) S(1, 0) ... S(N-1, 0)
The first line of a dataset consists of six integers, namely N, M, A, B, C and T. N is the number of cells. M is the modulus in the equation (1). A, B and C are coefficients in the equation (1). Finally, T is the time for which you should compute the states.
You may assume that 0 < N ≤ 50, 0 < M ≤ 1000, 0 ≤ A, B, C < M and 0 ≤ T ≤ 10^9.
The second line consists of N integers, each of which is non-negative and less than M. They represent the states of the cells at time zero.
A line containing six zeros indicates the end of the input.
Выходные данные
For each dataset, output a line that contains the states of the cells at time T. The format of the output is as follows.
S(0, T) S(1, T) ... S(N-1, T)
Each state must be represented as an integer and the integers must be separated by a space.
Пример
5 4 1 3 2 0 0 1 2 0 1 5 7 1 3 2 1 0 1 2 0 1 5 13 1 3 2 11 0 1 2 0 1 5 5 2 0 1 100 0 1 2 0 1 6 6 0 2 3 1000 0 1 2 0 1 4 20 1000 0 2 3 1000000000 0 1 2 0 1 0 1 2 0 1 0 1 2 0 1 0 1 2 0 1 30 2 1 0 1 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 30 2 1 1 1 1000000000 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 5 2 3 1 1000000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 2 0 1 2 0 0 4 3 2 12 10 9 11 3 0 4 2 1 0 4 2 0 4 4 0 376 752 0 376 0 376 752 0 376 0 376 752 0 376 0 376 752 0 376 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 2 2 3 3 1 4 3 1 2 3 0 4 3 3 0 4 2 2 2 2 1 1 2 1 3 0