#include <bits/stdc++.h>
using namespace std;
typedef vector< vector< int > > Matrix;
int Mod;

Matrix operator*(const Matrix& A, const Matrix& B)
{
  Matrix C(A.size(), vector< int >(B[0].size(), 0));
  for(int i = 0; i < A.size(); i++) {
    for(int k = 0; k < B.size(); k++) {
      for(int j = 0; j < B[0].size(); j++) {
        (C[i][j] += A[i][k] * B[k][j]) %= Mod;
      }
    }
  }
  return(C);
}
Matrix pow_mod(Matrix& A, int N)
{
  Matrix B(A.size(), vector< int >(A.size(), 0));
  for(int i = 0; i < A.size(); i++) B[i][i] = 1;
  while(N > 0) {
    if(N & 1) B = B * A;
    A = A * A;
    N >>= 1;
  }
  return(B);
}

int main()
{
  int N, A, B, C, T;
  while(cin >> N >> Mod >> A >> B >> C >> T, N) {
    Matrix x(N, vector< int >(N, 0)), y(N, vector< int >(1));
    for(int i = 0; i < N; i++) if(i > 0) x[i][i - 1] = A;
    for(int i = 0; i < N; i++) x[i][i] = B;
    for(int i = 0; i < N; i++) if(i + 1 < N) x[i][i + 1] = C;
    for(int i = 0; i < N; i++) cin >> y[i][0];
    x = pow_mod(x, T) * y;
    for(int i = 0; i < N; i++) cout << x[i][0] << (i != N - 1 ? " ": "\n");
  }
  
}
### Prompt

Your challenge is to write a cpp solution to the following problem:

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 defined 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 define S(i, t) = 0.

Given an automaton definition and initial states of cells, your mission is to write a program that computes the states of the cells at a specified time T.



Input

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 ≤ 109.

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.

Output

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.

Example

Input

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


Output

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef vector< vector< int > > Matrix;
int Mod;

Matrix operator*(const Matrix& A, const Matrix& B)
{
  Matrix C(A.size(), vector< int >(B[0].size(), 0));
  for(int i = 0; i < A.size(); i++) {
    for(int k = 0; k < B.size(); k++) {
      for(int j = 0; j < B[0].size(); j++) {
        (C[i][j] += A[i][k] * B[k][j]) %= Mod;
      }
    }
  }
  return(C);
}
Matrix pow_mod(Matrix& A, int N)
{
  Matrix B(A.size(), vector< int >(A.size(), 0));
  for(int i = 0; i < A.size(); i++) B[i][i] = 1;
  while(N > 0) {
    if(N & 1) B = B * A;
    A = A * A;
    N >>= 1;
  }
  return(B);
}

int main()
{
  int N, A, B, C, T;
  while(cin >> N >> Mod >> A >> B >> C >> T, N) {
    Matrix x(N, vector< int >(N, 0)), y(N, vector< int >(1));
    for(int i = 0; i < N; i++) if(i > 0) x[i][i - 1] = A;
    for(int i = 0; i < N; i++) x[i][i] = B;
    for(int i = 0; i < N; i++) if(i + 1 < N) x[i][i + 1] = C;
    for(int i = 0; i < N; i++) cin >> y[i][0];
    x = pow_mod(x, T) * y;
    for(int i = 0; i < N; i++) cout << x[i][0] << (i != N - 1 ? " ": "\n");
  }
  
}
```