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

Solution (in CPP):

Solution:
#include <valarray>
#include <cstdio>
using namespace std;
typedef valarray<int>V;
int N,M;
V mul(const V &a, const V &b){
    V c(N*N);
    int i=0,j;
    for(;i<N;i++)for(j=0;j<N;j++)c[i*N+j]=(a[slice(i*N,N,1)]*b[slice(j,N,N)]).sum()%M;
    return c;
}
V exp(const V &a, const int n){
    if(n==1)return a;
    if(n&1)return mul(exp(a,n-1),a);
    V b=exp(a,n>>1);
    return mul(b,b);
}
V s,x;
void output(const V &r){
    int i=0;
    for(;i<N-1;i++)printf("%d ",(r[slice(i*N,N,1)]*s).sum()%M);
    printf("%d\n",(r[slice(i*N,N,1)]*s).sum()%M);
}
int main(){
    int i,A,B,C,T;
    for(;scanf("%d%d%d%d%d%d",&N,&M,&A,&B,&C,&T),N;){
        s.resize(N);
        for(i=0;i<N;i++)scanf("%d",&s[i]);
        x.resize(0);
        x.resize(N*N);
        if(T){
            x[0]=B;
            x[1]=C;
            for(i=1;i<N-1;i++){
                x[i*N+i-1]=A;
                x[i*N+i]=B;
                x[i*N+i+1]=C;
            }
            x[i*N+i-1]=A;
            x[i*N+i]=B;
            output(exp(x,T));
        }else{
            for(i=0;i<N;i++)x[i*N+i]=1;
            output(x);
        }
    }
}