#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define inf (1<<29)

using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vvi matrix;

int N,M,A,B,C,T;

void init(matrix &mat)
{

  mat[N-1][N-2]             = A;
  mat[0][0] = mat[N-1][N-1] = B;
  mat[0][1]                 = C;
  REP(i,1,N-1)
    {
      mat[i][i-1] = A;
      mat[i][i] = B;
      mat[i][i+1] = C;
    }
}

matrix identity(int n)
{
  matrix A(n,vector<int>(n));
  for(int i=0;i<n;i++) A[i][i] = 1;
  return A;
}

matrix multi(const matrix& A,const matrix& B)
{
  matrix C(A.size(),vector<int>(B[0].size()));
  for(int i=0;i<C.size();++i)
    for(int j=0;j<C[i].size();++j)
      for(int k=0;k<A[i].size();++k)
	C[i][j] = (C[i][j]+(A[i][k]*B[k][j])%M)%M;
  return C;
}

matrix pow(const matrix& A,int e)
{
  return !e?identity(A.size()):
    (e%2?multi(A,pow(A,e-1)):pow(multi(A,A),e/2));
}

void print(matrix &mat)
{
  cout << "^^^^^^^^^^" << endl;
  rep(i,mat.size())
    {
      rep(j,mat[i].size())
	{
	  cout << mat[i][j] << " ";
	}
      cout << endl;
    }
  cout << "-------------" << endl;
}

int main()
{
  while(cin >> N >> M >> A >> B >> C >> T,N|M|A|B|C|T)
    {
      matrix s(N,vi(1));
      rep(i,N)cin >> s[i][0];
      matrix coef(N,vi(N,0));
      init(coef);
      coef = pow(coef,T);
      s = multi(coef,s);
      rep(i,N)cout << (i?" ":"") << s[i][0];
      cout << endl;
    }
  return 0;
}
### Prompt

Your task is to create 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<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define inf (1<<29)

using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vvi matrix;

int N,M,A,B,C,T;

void init(matrix &mat)
{

  mat[N-1][N-2]             = A;
  mat[0][0] = mat[N-1][N-1] = B;
  mat[0][1]                 = C;
  REP(i,1,N-1)
    {
      mat[i][i-1] = A;
      mat[i][i] = B;
      mat[i][i+1] = C;
    }
}

matrix identity(int n)
{
  matrix A(n,vector<int>(n));
  for(int i=0;i<n;i++) A[i][i] = 1;
  return A;
}

matrix multi(const matrix& A,const matrix& B)
{
  matrix C(A.size(),vector<int>(B[0].size()));
  for(int i=0;i<C.size();++i)
    for(int j=0;j<C[i].size();++j)
      for(int k=0;k<A[i].size();++k)
	C[i][j] = (C[i][j]+(A[i][k]*B[k][j])%M)%M;
  return C;
}

matrix pow(const matrix& A,int e)
{
  return !e?identity(A.size()):
    (e%2?multi(A,pow(A,e-1)):pow(multi(A,A),e/2));
}

void print(matrix &mat)
{
  cout << "^^^^^^^^^^" << endl;
  rep(i,mat.size())
    {
      rep(j,mat[i].size())
	{
	  cout << mat[i][j] << " ";
	}
      cout << endl;
    }
  cout << "-------------" << endl;
}

int main()
{
  while(cin >> N >> M >> A >> B >> C >> T,N|M|A|B|C|T)
    {
      matrix s(N,vi(1));
      rep(i,N)cin >> s[i][0];
      matrix coef(N,vi(N,0));
      init(coef);
      coef = pow(coef,T);
      s = multi(coef,s);
      rep(i,N)cout << (i?" ":"") << s[i][0];
      cout << endl;
    }
  return 0;
}
```