#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<27;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-11;
//const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

ll mod;

vvl mul(vvl A,vvl B){
	vvl C(A.size(),vl(B[0].size()));
	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;
}

// 行列の最小二乗法
vvl pow(vvl A,ll n){
	vvl B(A.size(),vl(A.size()));
	for(int i=0;i<A.size();i++) B[i][i]=1;
	while(n>0){
		if(n&1) B=mul(B,A);
		A=mul(A,A);
		n>>=1;
	}
	return B;
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	while(1){
		int n,m,a,b,c,t;
		cin>>n>>m>>a>>b>>c>>t;
		if(n==0) break;
		mod=m;
		vi d(n);
		for(int i=0;i<n;i++) cin>>d[i];
		vvl A(n,vl(n));
		for(int i=0;i<n;i++){
			if(i+1<n) A[i+1][i]=a;
			A[i][i]=b;
			if(i) A[i-1][i]=c;
		}
		A=pow(A,t);
		for(int i=0;i<n;i++){
			if(i) cout<<' ';
			ll res=0;
			for(int j=0;j<n;j++) (res+=A[i][j]*d[j])%=mod;
			cout<<res;
		}
		cout<<endl;
	}
}

### Prompt

Create a solution in Cpp for 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>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<27;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-11;
//const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

ll mod;

vvl mul(vvl A,vvl B){
	vvl C(A.size(),vl(B[0].size()));
	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;
}

// 行列の最小二乗法
vvl pow(vvl A,ll n){
	vvl B(A.size(),vl(A.size()));
	for(int i=0;i<A.size();i++) B[i][i]=1;
	while(n>0){
		if(n&1) B=mul(B,A);
		A=mul(A,A);
		n>>=1;
	}
	return B;
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	while(1){
		int n,m,a,b,c,t;
		cin>>n>>m>>a>>b>>c>>t;
		if(n==0) break;
		mod=m;
		vi d(n);
		for(int i=0;i<n;i++) cin>>d[i];
		vvl A(n,vl(n));
		for(int i=0;i<n;i++){
			if(i+1<n) A[i+1][i]=a;
			A[i][i]=b;
			if(i) A[i-1][i]=c;
		}
		A=pow(A,t);
		for(int i=0;i<n;i++){
			if(i) cout<<' ';
			ll res=0;
			for(int j=0;j<n;j++) (res+=A[i][j]*d[j])%=mod;
			cout<<res;
		}
		cout<<endl;
	}
}

```