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 JAVA):

Solution:
import java.util.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class Main {

	Scanner sc = new Scanner(in);
	
	int[][] A = new int[50][50];
	int[][] B = new int[50][50];
	int[][] T = new int[50][50];
	int n, mod;
	
	void mult(int[][] C, int[][] D) {
		for (int i = 0; i < n; i++)
			Arrays.fill(T[i], 0);
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				for (int k = 0; k < n; k++) {
					T[i][j] = (T[i][j] + C[i][k]*D[k][j]) % mod;
				}
			}
		}
	}
	
	void subst(int[][] C, int[][] D) {
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				C[i][j] = D[i][j];
			}
		}
	}
	
	void pow(int t) {
		for (int i = 0; i < n; i++) {
			Arrays.fill(B[i], 0);
			B[i][i] = 1;
		}
		while (t > 0) {
			if ((t & 1) == 1) {
				mult(A, B);
				subst(B, T);
			}
			mult(A, A);
			subst(A, T);
			t >>= 1;
		}
	}
	
	void run() {
		int[] stat = new int[50];
		while (true) {
			n = sc.nextInt();
			mod = sc.nextInt();
			int a = sc.nextInt(), b = sc.nextInt(), c = sc.nextInt();
			int t = sc.nextInt();
			if (n == 0) break;

			for (int i = 0; i < n; i++)
				stat[i] = sc.nextInt();
			
			Arrays.fill(A[0], 0);
			A[0][0] = b; A[0][1] = c;
			for (int i = 1; i < n-1; i++) {
				Arrays.fill(A[i], 0);
				A[i][i-1] = a;
				A[i][i] = b;
				A[i][i+1] = c;
			}
			Arrays.fill(A[n-1], 0);
			A[n-1][n-2] = a;
			A[n-1][n-1] = b;
			
			pow(t);
			
			int res = 0;
			for (int i = 0; i < n; i++) {
				res = (res + B[0][i]*stat[i]) % mod;
			}
			out.print(res);
			for (int i = 1; i < n; i++) {
				res = 0;
				for (int j = 0; j < n; j++) {
					res = (res + B[i][j]*stat[j]) % mod;
				}
				out.printf(" %d", res);
			}
			out.println();
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}

}