#include <bits/stdc++.h>
using namespace std;
void m_mul(vector<vector<vector<int>>> &table,int n,int d,int m){
    int i,j,k;
    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            table[d+1][i][j]=0;
            for(k=0;k<n;k++){
                table[d+1][i][j]+=table[d][i][k]*table[d][k][j];
            }
            table[d+1][i][j]%=m;
        }
    }
}

vector<int> mul(vector<int> A, vector<vector<int>> table,int n,int m){
    int i,j;
    vector<int> ans(n);
    for(i=0;i<n;i++){
        ans[i]=0;
        for(j=0;j<n;j++){
            ans[i]+=A[j]*table[i][j];
        }
        ans[i]%=m;
    }
    return ans;
}

int main(void){
    int n,m,a,b,c,t;
    while(cin>>n>>m>>a>>b>>c>>t,n){
        int i;
        vector<vector<vector<int>>> table(31,vector<vector<int>>(50,vector<int>(50)));
        for(i=0;i<n;i++){
            if(i-1>=0) table[0][i][i-1] = a;
            table[0][i][i] = b;
            if(i+1<n) table[0][i][i+1] = c;
        }
        int d=0;
        for(i=2;i<=t;i*=2){
            m_mul(table,n,d,m);
            d++;
        }
        vector<int> ans(n);
        for(i=0;i<n;i++){
            cin>>ans[i];
        }
        for(i=0;t!=0;t/=2,i++){
            if(t%2==1){
                ans=mul(ans,table[i],n,m);
            }
        }
        for(int z=0;z<n;z++){
            cout<<ans[z];
            if(z+1==n){
                cout<<endl;
            }else{
                cout<<' ';
            }
        }
    }
}


### Prompt

Please formulate 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;
void m_mul(vector<vector<vector<int>>> &table,int n,int d,int m){
    int i,j,k;
    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            table[d+1][i][j]=0;
            for(k=0;k<n;k++){
                table[d+1][i][j]+=table[d][i][k]*table[d][k][j];
            }
            table[d+1][i][j]%=m;
        }
    }
}

vector<int> mul(vector<int> A, vector<vector<int>> table,int n,int m){
    int i,j;
    vector<int> ans(n);
    for(i=0;i<n;i++){
        ans[i]=0;
        for(j=0;j<n;j++){
            ans[i]+=A[j]*table[i][j];
        }
        ans[i]%=m;
    }
    return ans;
}

int main(void){
    int n,m,a,b,c,t;
    while(cin>>n>>m>>a>>b>>c>>t,n){
        int i;
        vector<vector<vector<int>>> table(31,vector<vector<int>>(50,vector<int>(50)));
        for(i=0;i<n;i++){
            if(i-1>=0) table[0][i][i-1] = a;
            table[0][i][i] = b;
            if(i+1<n) table[0][i][i+1] = c;
        }
        int d=0;
        for(i=2;i<=t;i*=2){
            m_mul(table,n,d,m);
            d++;
        }
        vector<int> ans(n);
        for(i=0;i<n;i++){
            cin>>ans[i];
        }
        for(i=0;t!=0;t/=2,i++){
            if(t%2==1){
                ans=mul(ans,table[i],n,m);
            }
        }
        for(int z=0;z<n;z++){
            cout<<ans[z];
            if(z+1==n){
                cout<<endl;
            }else{
                cout<<' ';
            }
        }
    }
}


```