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.Arrays;
import java.util.Scanner;

public class Main {

	public static final void main(String[] args) {
		new Main();
	}

	public Main() {
		Scanner sc = new Scanner(System.in);
		while(true){
			int n = sc.nextInt();
			int m = sc.nextInt();
			int a = sc.nextInt();
			int b = sc.nextInt();
			int c = sc.nextInt();
			int t = sc.nextInt();
			if(n==0 && m==0 && a==0 && b==0 && c==0 && t==0)
				break;
			
			int[] s = new int[n];
			for(int i=0;i<n;i++)
				s[i] = sc.nextInt();
	
			solve(n, m, a, b, c, t, s);
		}
		sc.close();
	}

	private void solve(int n, int m, int a, int b, int c, int t, int[] s) {
		int[][] mat = new int[n][n];
		
		for(int i=1;i<n;i++)
			mat[i][i-1] = a;
		for(int i=0;i<n;i++)
			mat[i][i] = b;
		for(int i=0;i<n-1;i++)
			mat[i][i+1] = c;
		
		mat = mulMat(mat, t, m);
//		for(int i=0;i<mat.length;i++)
//			System.out.println(Arrays.toString(mat[i]));
		
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<n;i++){
			int sum = 0;
			for(int j=0;j<n;j++){
				sum += mat[i][j]*s[j];
				sum %= m;
			}
			sb.append(sum).append(' ');
		}
		sb.deleteCharAt(sb.length()-1);
		System.out.println(sb.toString());
		
	}
	
	private int[][] mulMat(int[][] mat, int mult, int mod){
		int n = mat.length;
		int[][] retMat = new int[n][n];
		for(int i=0;i<n;i++)
			retMat[i][i] = 1;
		
		int c = 1;
		while(c<=mult){
			if((c&mult) > 0){
				retMat = mulMat(retMat, mat, mod);
			}
			mat = mulMat(mat, mat, mod);
			
			c*=2;
		}
		return retMat;
	}
	
	/** mat1???????????\??? */
	private int[][] mulMat(int[][] mat1, int[][] mat2, int mod){
		int n = mat1.length;
		int[][] retMat = new int[n][n];
		
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				int sum = 0;
				for(int k=0;k<n;k++)
					sum += mat1[i][k]*mat2[k][j];
				retMat[i][j] = sum%mod;
			}
		}
		return retMat;
	}
	
}