#include <iostream>
#include <vector>
using namespace std;

long long int N, M;

typedef vector< vector<long long int> > matrix;

matrix mul(matrix a, matrix b)
{
	matrix res(N, vector<long long int>(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] += a[k][j] * b[i][k];
			}
			if(res[i][j] >= M)
				res[i][j] %= M;
		}
	}
	return res;
}

matrix pow(matrix m, int n)
{
	matrix res(N, vector<long long int>(N, 0));
	for (int i = 0; i < N; i++)
		res[i][i] = 1;
	int x = 1;
	while (x <= n) {
		if ((x & n) > 0) {
			res = mul(res, m);
		}
		m = mul(m, m);
		x <<= 1;
	}
	return res;
}

int main()
{
	long long int A, B, C, T;
	while (cin >> N >> M >> A >> B >> C >> T, N | M | A | B | C | T) {
		matrix bottom(N,vector<long long int>(N,0)),mat(N, vector<long long int>(N, 0)),res;
		for (int i = 0; i < N; i++) {
			if (i - 1 >= 0) {
				bottom[i][i - 1] = A;
			}
			bottom[i][i] = B;
			if (i + 1 < N) {
				bottom[i][i + 1] = C;
			}
		}
		for (int i = 0; i < N; i++) {
			cin >> mat[i][N - 1];
		}
		res = mul(mat, pow(bottom, T));
		for (int i = 0; i < N; i++) {
			cout << res[i][N - 1];
			if (i + 1 < N)
				cout << " ";
			else
				cout << endl;
		}
	}
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 <vector>
using namespace std;

long long int N, M;

typedef vector< vector<long long int> > matrix;

matrix mul(matrix a, matrix b)
{
	matrix res(N, vector<long long int>(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] += a[k][j] * b[i][k];
			}
			if(res[i][j] >= M)
				res[i][j] %= M;
		}
	}
	return res;
}

matrix pow(matrix m, int n)
{
	matrix res(N, vector<long long int>(N, 0));
	for (int i = 0; i < N; i++)
		res[i][i] = 1;
	int x = 1;
	while (x <= n) {
		if ((x & n) > 0) {
			res = mul(res, m);
		}
		m = mul(m, m);
		x <<= 1;
	}
	return res;
}

int main()
{
	long long int A, B, C, T;
	while (cin >> N >> M >> A >> B >> C >> T, N | M | A | B | C | T) {
		matrix bottom(N,vector<long long int>(N,0)),mat(N, vector<long long int>(N, 0)),res;
		for (int i = 0; i < N; i++) {
			if (i - 1 >= 0) {
				bottom[i][i - 1] = A;
			}
			bottom[i][i] = B;
			if (i + 1 < N) {
				bottom[i][i + 1] = C;
			}
		}
		for (int i = 0; i < N; i++) {
			cin >> mat[i][N - 1];
		}
		res = mul(mat, pow(bottom, T));
		for (int i = 0; i < N; i++) {
			cout << res[i][N - 1];
			if (i + 1 < N)
				cout << " ";
			else
				cout << endl;
		}
	}
	return 0;
}
```