Problem:
Problem C: One-Dimensional Cellular Automaton

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.

Sample 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 for the Sample Input

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 C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

template<class T>
bool chmax(T& a, const T& b) {
    if (a < b) { a = b; return true; }
    return false;
}
template<class T>
bool chmin(T& a, const T& b) {
    if (b < a) { a = b; return true; }
    return false;
}

// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

// std::vector Declaration and Initialization
template<typename T>
vector<T> make_vector(size_t a, T x) { return vector<T>(a, x); }
template<typename T, typename U, typename... Ts>
auto make_vector(size_t a, U b, Ts... ts) {
    return vector<decltype(make_vector<T>(b,ts...))>(a, make_vector<T>(b, ts...));
}

// std::vector Input
template<typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (auto &e : v) is >> e;
    return is;
}

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::array Debug
template<typename T, size_t n>
ostream& operator<<(ostream& os, const array<T, n>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::deque Debug
template<typename T>
ostream& operator<<(ostream& os, const deque<T>& d) {
    os << "[";
    bool a = 1;
    for (auto e : d) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << " " << p.second << ")";
    return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::multiset Debug
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
    os << "{";
    bool a = 1;
    for (auto e : mp) {
        os << (a ? "" : " ");
        os << e.first << ":" << e.second;
        a = 0;
    }
    os << "}";
    return os;
}

// std::tuple Debug
template<int N, class Tuple>
void out(ostream& os, const Tuple& t){}
template<int N, class Tuple, class H, class ...Ts>
void out(ostream& os, const Tuple& t) {
    if (N) os << " ";
    os << get<N>(t);
    out<N+1,Tuple,Ts...>(os, t);
}
template<class ...Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
    os << "(";
    out<0,tuple<Ts...>,Ts...>(os, t);
    os << ")";
    return os;
}

// Debug
#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl

// Weighted edge
template<typename T>
struct edge {
    int src, to;
    T cost;

    edge() {}
    edge(int to, T cost) : src(-1), to(to), cost(cost) {}
    edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

    friend ostream& operator<<(ostream& os, const edge& e) {
        return os << "(" << e.src << "->" << e.to << ":" << e.cost << ")";
    }
};

using LL = long long;

#define fs first
#define sc second

const LL MOD = 1e9+7;


template<typename T>
struct Matrix {
    vector<vector<T>> A;

    Matrix() {}

    Matrix(size_t n, size_t m) : A(n, vector<T>(m)) {}

    Matrix(size_t n) : A(n, vector<T>(n)) {};

    size_t height() const {
        return (A.size());
    }

    size_t width() const {
        return (A[0].size());
    }

    inline const vector<T> &operator[](int k) const {
        return (A.at(k));
    }

    inline vector<T> &operator[](int k) {
        return (A.at(k));
    }

    static Matrix I(size_t n) {
        Matrix B(n);
        for (int i = 0; i < n; i++) B[i][i] = 1;
        return (B);
    }

    Matrix operator-() const {
        size_t n = height(), m = width();
        Matrix B = *this;
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
                B[i][j] = -B[i][j];
        return (B);
    }

    Matrix& operator+=(const Matrix& B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                A[i][j] += B[i][j];
        return (*this);
    }

    Matrix& operator-=(const Matrix& B) {
        return (*this += -B);
    }

    Matrix& operator*=(const Matrix& B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        Matrix C(n, m);
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                for(int k = 0; k < p; k++)
                    C[i][j] += A[i][k] * B[k][j];
        A.swap(C.A);
        return (*this);
    }

    Matrix pow(int64_t k) {
        Matrix B = Matrix::I(height()), tmp = *this;
        while (k > 0) {
            if (k & 1) B *= tmp;
            tmp *= tmp;
            k >>= 1LL;
        }
        return (B);
    }

    const Matrix operator+(const Matrix& B) const {
        return (Matrix(*this) += B);
    }

    const Matrix operator-(const Matrix& B) const {
        return (Matrix(*this) -= B);
    }

    const Matrix operator*(const Matrix& B) const {
        return (Matrix(*this) *= B);
    }

    int GaussJordanElimination() {
        int rank = 0;
        for (int col = 0; col < width(); ++col) {
            int pivot = -1;
            for (int row = rank; row < height(); ++row) {
                if (A[row][col] != 0) {
                    pivot = row;
                    break;
                }
            }
            if (pivot == -1) continue;
            swap(A[rank], A[pivot]);
            T topLeft = A[rank][col];
            for (int c = col; c < width(); ++c) {
                A[rank][c] /= topLeft;
            }
            for (int row = rank+1; row < height(); ++row) {
                T ratio = A[row][col];
                for (int c = col; c < width(); ++c)
                    A[row][c] -= ratio * A[rank][c];
            }
            ++rank;
        }
        return (rank);
    }

    friend istream& operator>>(istream& is, Matrix& B) {
        is >> B.A;
        return (is);
    }

    friend ostream& operator<<(ostream& os, Matrix& B) {
        size_t n = B.height(), m = B.width();
        for(int i = 0; i < n; i++) {
            os << (i == 0 ? "[" : " ");
            for(int j = 0; j < m; j++) {
                os << B[i][j] << (j == m-1 ? "]" : ",");
            }
            os << (i == n-1 ? "]\n" : ",\n");
        }
        return (os);
    }
};

int mod[] = {MOD};

struct modint {
    using LL = int64_t;
    LL val;
    modint(LL val=0) : val(((val % mod[0]) + mod[0]) % mod[0]) {}

    const modint operator+() const { return *this; }
    const modint operator-() const { return (-val + mod[0]) % mod[0]; }
    const modint inv() const { return pow(mod[0]-2); }

    modint& operator+=(const modint& rhs) {
        (val += rhs.val) %= mod[0];
        return *this;
    }
    modint& operator-=(const modint& rhs) {
        return *this += -rhs;
    }
    modint& operator*=(const modint& rhs) {
        (val *= rhs.val) %= mod[0];
        return *this;
    }
    modint& operator/=(const modint& rhs) {
        return *this *= rhs.inv();
    }

    const modint operator+(const modint& rhs) const {
        return modint(*this) += rhs;
    }
    const modint operator-(const modint& rhs) const {
        return modint(*this) -= rhs;
    }
    const modint operator*(const modint& rhs) const {
        return modint(*this) *= rhs;
    }
    const modint operator/(const modint& rhs) const {
        return modint(*this) /= rhs;
    }

    const modint pow(LL n) const {
        modint ret = 1, tmp = val;
        while (n > 0) {
            if (n & 1) ret *= tmp;
            tmp *= tmp; n >>= 1;
        }
        return ret;
    }

    bool operator==(const modint& rhs) const { return val == rhs.val; }
    bool operator!=(const modint& rhs) const { return !(*this == rhs); }

    friend const modint operator+(const LL& lhs, const modint& rhs) {
        return modint(lhs) + rhs;
    }
    friend const modint operator-(const LL& lhs, const modint& rhs) {
        return modint(lhs) - rhs;
    }
    friend const modint operator*(const LL& lhs, const modint& rhs) {
        return modint(lhs) * rhs;
    }
    friend const modint operator/(const LL& lhs, const modint& rhs) {
        return modint(lhs) / rhs;
    }

    friend bool operator==(const LL& lhs, const modint& rhs) {
        return modint(lhs) == rhs;
    }
    friend bool operator!=(const LL& lhs, const modint& rhs) {
        return modint(lhs) != rhs;
    }

    friend ostream& operator<<(ostream& os, const modint& a) {
        return os << a.val;
    }
    friend istream& operator>>(istream& is, modint& a) {
        LL tmp; is >> tmp;
        a = tmp;
        return is;
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);

    while (true) {
        int N, M, A, B, C, T;
        cin >> N >> M >> A >> B >> C >> T;
        if (N == 0) {
            break;
        }
        mod[0] = M;
        auto S = Matrix<modint>(N, 1);
        cin >> S;

        auto mat = Matrix<modint>(N, N);
        for (int i = 0; i < N; ++i) {
            if (i-1 >= 0) mat[i][i-1] = A;
            if (i+1 < N) mat[i][i+1] = C;
            mat[i][i] = B;
        }

        S = mat.pow(T) * S;

        for (int i = 0; i < N; ++i) {
            if (i) cout << " ";
            cout << S[i][0];
        }
        cout << endl;
    }

    return 0;
}