#include <bits/stdc++.h>
using namespace std;
#define int long long   // <-----!!!!!!!!!!!!!!!!!!!

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()

typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> V;
typedef vector<V> VV;
typedef vector<VV> VVV;
typedef vector<vector<int>> Graph;
typedef vector<vector<int>> Mat;
const int inf = 1e9;
const int mod = 1e9 + 7;

int N, M, A, B, C, T;

Mat mulMatMat(const Mat& a, const Mat& b) {
    int n = a.size();
    int m = b[0].size();
    assert(a[0].size() == b.size());
    Mat c(n, V(m, 0));
    rep(i, n) {
        rep(j, m) {
            rep(k, a[0].size()) {
                (c[i][j] += a[i][k] * b[k][j]) %= M;
            }
        }
    }
    return c;
}

V mulMatVec(const Mat& a, const V& v) {
    int n = a.size();
    assert(a[0].size() == v.size());
    V c(n, 0);
    rep(i, n) {
        rep(j, a[0].size()) {
            (c[i] += a[i][j] * v[j]) %= M;
        }
    }
    return c;
}

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

    while (cin >> N >> M >> A >> B >> C >> T, N) {
        V s(N + 2);
        rep2(i, 1, N + 1) cin >> s[i];

        VV a(N + 2, V(N + 2));
        rep2(i, 1, N + 1) {
            a[i][i - 1] = A,    a[i][i] = B,    a[i][i + 1] = C;
        }

        for (; T > 0; T >>= 1) {
            if (T & 1) {
                s = mulMatVec(a, s);
            }
            a = mulMatMat(a, a);
        }

        rep2(i, 1, N + 1) {
            cout << (i != 1 ? " " : "") << s[i];
        }
        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 <bits/stdc++.h>
using namespace std;
#define int long long   // <-----!!!!!!!!!!!!!!!!!!!

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()

typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> V;
typedef vector<V> VV;
typedef vector<VV> VVV;
typedef vector<vector<int>> Graph;
typedef vector<vector<int>> Mat;
const int inf = 1e9;
const int mod = 1e9 + 7;

int N, M, A, B, C, T;

Mat mulMatMat(const Mat& a, const Mat& b) {
    int n = a.size();
    int m = b[0].size();
    assert(a[0].size() == b.size());
    Mat c(n, V(m, 0));
    rep(i, n) {
        rep(j, m) {
            rep(k, a[0].size()) {
                (c[i][j] += a[i][k] * b[k][j]) %= M;
            }
        }
    }
    return c;
}

V mulMatVec(const Mat& a, const V& v) {
    int n = a.size();
    assert(a[0].size() == v.size());
    V c(n, 0);
    rep(i, n) {
        rep(j, a[0].size()) {
            (c[i] += a[i][j] * v[j]) %= M;
        }
    }
    return c;
}

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

    while (cin >> N >> M >> A >> B >> C >> T, N) {
        V s(N + 2);
        rep2(i, 1, N + 1) cin >> s[i];

        VV a(N + 2, V(N + 2));
        rep2(i, 1, N + 1) {
            a[i][i - 1] = A,    a[i][i] = B,    a[i][i + 1] = C;
        }

        for (; T > 0; T >>= 1) {
            if (T & 1) {
                s = mulMatVec(a, s);
            }
            a = mulMatMat(a, a);
        }

        rep2(i, 1, N + 1) {
            cout << (i != 1 ? " " : "") << s[i];
        }
        cout << endl;

    }
}
```