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 <iostream>
#include <algorithm>

using namespace std;

const int N = 50;

void mult(int m1[N][N], int m2[N][N], int n, int m){
  int res[N][N];
  fill(res[0], res[N], 0);
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      for(int k=0;k<n;k++) res[i][j] = (res[i][j] + m1[i][k] * m2[k][j]) % m;
    }
  }
  for(int i=0;i<n;i++) for(int j=0;j<n;j++) m1[i][j] = res[i][j];
}

void mod_pow(int mat[N][N], int p, int n, int m){
  int res[N][N];
  fill(res[0], res[N], 0);
  for(int i=0;i<n;i++) res[i][i] = 1;
  while(p > 0){
    if(p & 1) mult(res, mat, n, m);
    mult(mat, mat, n, m);
    p >>= 1;
  }
  for(int i=0;i<n;i++) for(int j=0;j<n;j++) mat[i][j] = res[i][j];
}

int main(){
  int n, m, a, b ,c, t, s[N], mat[N][N];
  while(cin >> n >> m >> a >> b >> c >> t && (n|m|a|b|c|t)){
    for(int i=0;i<n;i++) cin >> s[i];
    fill(mat[0], mat[N], 0);
    for(int i=0;i<n;i++){
      if(i - 1 >= 0) mat[i][i-1] = a;
      mat[i][i] = b;
      if(i + 1 < n) mat[i][i+1] = c;
    }
    mod_pow(mat, t, n, m);
    for(int i=0;i<n;i++){
      int ans = 0;
      for(int j=0;j<n;j++) ans = (ans + mat[i][j] * s[j]) % m;
      if(i) cout << " ";
      cout << ans;
    }
    cout << endl;
  }
}