#include <iostream>
#include <sstream>
#include <string>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cassert>

using namespace std;

#define FOR(i,k,n) for(int i=(k); i<(int)(n); ++i)
#define REP(i,n) FOR(i,0,n)
#define FORIT(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)

template<class T> void debug(T begin, T end){ for(T i = begin; i != end; ++i) cerr<<*i<<" "; cerr<<endl; }
inline bool valid(int x, int y, int W, int H){ return (x >= 0 && y >= 0 && x < W && y < H); }

typedef long long ll;
const int INF = 100000000;
const double EPS = 1e-8;
const int MOD = 1000000007;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
typedef vector<int> Array;
typedef vector<Array> Matrix;
Matrix mul(const Matrix& m, const Matrix& n, int M){
  int N = m.size();
  Matrix res(N, Array(N));
  REP(i, N)REP(j, N)REP(k, N){
    res[i][j] += m[i][k] * n[k][j];
    res[i][j] %= M;
  }
  return res;
}
Matrix make_E(int N){
  Matrix res(N, Array(N));
  REP(i, N) res[i][i] = 1;
  return res;
}
Matrix pow(const Matrix& m, int p, int M){
  int N = m.size();
  if(p == 0) return make_E(N);
  if(p == 1) return m;
  if(p & 1){
    return mul(m, pow(mul(m, m, M), p / 2, M), M);
  }else{
    return pow(mul(m, m, M), p / 2, M);
  }
}

int main(){
  int N, M, A, B, C, T;
  while(cin>>N>>M>>A>>B>>C>>T){
    vector<int> S(N);
    REP(i, N) cin>>S[i];
    Matrix m(N, Array(N));
    REP(i, N)REP(j, N){
      if(i - 1 == j) m[i][j] = A;
      else if(i     == j) m[i][j] = B;
      else if(i + 1 == j) m[i][j] = C;
      else m[i][j] = 0;
    }
    m = pow(m, T, M);
    REP(i, N){
      int ans = 0;
      REP(j, N){
        ans += m[i][j] * S[j];
        ans %= M;
      }
      cout<<ans;
      if(i == N - 1) cout<<endl;
      else cout<<" ";
    }
  }

  return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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 <sstream>
#include <string>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cassert>

using namespace std;

#define FOR(i,k,n) for(int i=(k); i<(int)(n); ++i)
#define REP(i,n) FOR(i,0,n)
#define FORIT(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)

template<class T> void debug(T begin, T end){ for(T i = begin; i != end; ++i) cerr<<*i<<" "; cerr<<endl; }
inline bool valid(int x, int y, int W, int H){ return (x >= 0 && y >= 0 && x < W && y < H); }

typedef long long ll;
const int INF = 100000000;
const double EPS = 1e-8;
const int MOD = 1000000007;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
typedef vector<int> Array;
typedef vector<Array> Matrix;
Matrix mul(const Matrix& m, const Matrix& n, int M){
  int N = m.size();
  Matrix res(N, Array(N));
  REP(i, N)REP(j, N)REP(k, N){
    res[i][j] += m[i][k] * n[k][j];
    res[i][j] %= M;
  }
  return res;
}
Matrix make_E(int N){
  Matrix res(N, Array(N));
  REP(i, N) res[i][i] = 1;
  return res;
}
Matrix pow(const Matrix& m, int p, int M){
  int N = m.size();
  if(p == 0) return make_E(N);
  if(p == 1) return m;
  if(p & 1){
    return mul(m, pow(mul(m, m, M), p / 2, M), M);
  }else{
    return pow(mul(m, m, M), p / 2, M);
  }
}

int main(){
  int N, M, A, B, C, T;
  while(cin>>N>>M>>A>>B>>C>>T){
    vector<int> S(N);
    REP(i, N) cin>>S[i];
    Matrix m(N, Array(N));
    REP(i, N)REP(j, N){
      if(i - 1 == j) m[i][j] = A;
      else if(i     == j) m[i][j] = B;
      else if(i + 1 == j) m[i][j] = C;
      else m[i][j] = 0;
    }
    m = pow(m, T, M);
    REP(i, N){
      int ans = 0;
      REP(j, N){
        ans += m[i][j] * S[j];
        ans %= M;
      }
      cout<<ans;
      if(i == N - 1) cout<<endl;
      else cout<<" ";
    }
  }

  return 0;
}
```