#include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr double EPS = 1e-12;

//int N, M, K, T, H, W, L, R;
long long int N, M, K, T, H, W, L, R;

vector<vector<long long int>>matrix_product(vector<vector<long long int>>v, vector<vector<long long int>>w) {
	vector<vector<long long int>>ret(v.size(), vector<long long int>(w.front().size()));
	for (int i = 0; i < ret.size(); i++) {
		for (int j = 0; j < ret[i].size(); j++) {
			for (int k = 0; k < w.size(); k++) {
				ret[i][j] += v[i][k] * w[k][j];
				ret[i][j] %= M;
			}
		}
	}
	return ret;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int a, b, c;
	while (cin >> N >> M >> a >> b >> c >> T, N) {
		vector<int>v(N);
		for (auto &i : v)cin >> i;
		vector<vector<long long int>>by(N, vector<long long int>(N));
		for (int i = 0; i < N; i++)by[i][i] = 1;
		vector<vector<long long int>>box(N, vector<long long int>(N));
		for (int i = 0; i < N; i++) {
			if (i) {
				box[i][i - 1] = a;
			}
			box[i][i] = b;
			if (i + 1 < N)box[i][i + 1] = c;
		}
		for (int i = 0; i < 30; i++) {
			if ((T >> i) & 1) {
				by = matrix_product(box, by);
			}
			box = matrix_product(box, box);
		}
		vector<vector<long long int>>ans(N, vector<long long int>(1));
		for (int i = 0; i < N; i++) {
			ans[i][0] = v[i];
		}
		ans = matrix_product(by, ans);
		for (int i = 0; i < N; i++) {
			if (i)cout << " ";
			cout << ans[i][0];
		}
		cout << endl;
	}
}

### Prompt

Develop a solution in CPP to the problem described below:

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 "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr double EPS = 1e-12;

//int N, M, K, T, H, W, L, R;
long long int N, M, K, T, H, W, L, R;

vector<vector<long long int>>matrix_product(vector<vector<long long int>>v, vector<vector<long long int>>w) {
	vector<vector<long long int>>ret(v.size(), vector<long long int>(w.front().size()));
	for (int i = 0; i < ret.size(); i++) {
		for (int j = 0; j < ret[i].size(); j++) {
			for (int k = 0; k < w.size(); k++) {
				ret[i][j] += v[i][k] * w[k][j];
				ret[i][j] %= M;
			}
		}
	}
	return ret;
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int a, b, c;
	while (cin >> N >> M >> a >> b >> c >> T, N) {
		vector<int>v(N);
		for (auto &i : v)cin >> i;
		vector<vector<long long int>>by(N, vector<long long int>(N));
		for (int i = 0; i < N; i++)by[i][i] = 1;
		vector<vector<long long int>>box(N, vector<long long int>(N));
		for (int i = 0; i < N; i++) {
			if (i) {
				box[i][i - 1] = a;
			}
			box[i][i] = b;
			if (i + 1 < N)box[i][i + 1] = c;
		}
		for (int i = 0; i < 30; i++) {
			if ((T >> i) & 1) {
				by = matrix_product(box, by);
			}
			box = matrix_product(box, box);
		}
		vector<vector<long long int>>ans(N, vector<long long int>(1));
		for (int i = 0; i < N; i++) {
			ans[i][0] = v[i];
		}
		ans = matrix_product(by, ans);
		for (int i = 0; i < N; i++) {
			if (i)cout << " ";
			cout << ans[i][0];
		}
		cout << endl;
	}
}

```