#include <iostream>#include <algorithm>#include <vector>#include <cmath>using namespace std;#define LL long long#define MAX_N 20 + 8int A, B, N, M;LL C[MAX_N][MAX_N];void build_combinatorial_number() { for (int i = 0; i < MAX_N; ++i) { C[i][0] = C[i][i] = 1; for (int j = 1; j < i; ++j) C[i][j] = C[i - 1][j - 1] + C[i - 1][j]; }}inline int to_index(int n, int m) { return n * M + m + 1;}vector<double> gauss(vector< vector<double> >& A) { int n = A.size(); for (int i = 0; i < n; ++i) { double maxEl = abs(A[i][i]); int maxRow = i; for (int k = i + 1; k < n; ++k) { if (abs(A[k][i]) > maxEl) { maxEl = abs(A[k][i]); maxRow = k; } } for (int k = i; k < n + 1; ++k) { double tmp = A[maxRow][k]; A[maxRow][k] = A[i][k]; A[i][k] = tmp; } for (int k = i + 1; k < n; ++k) { double c = -A[k][i] / A[i][i]; for (int j = i; j < n + 1; ++j) { if (i == j) { A[k][j] = 0; } else { A[k][j] += c * A[i][j]; } } } } vector<double> x(n); for (int i = n - 1; i >= 0; --i) { x[i] = A[i][n] / A[i][i]; for (int k = i - 1; k >= 0; --k) { A[k][n] -= A[k][i] * x[i]; } } return x;}inline double round(double x){ return x >= 0.0 ? floor(x + 0.5) : ceil(x - 0.5);}void solve() { const int size = N * M + 1; vector< vector<double> > mat(size, vector<double>(size + 1, 0.0)); mat[0][0] = 1.0; mat[0][size] = 1.0; for (int d = 0; d < size; ++d) { for (int k = 0; k <= d; ++k) { mat[to_index(k % N, (d - k) % M)][d < N * M ? d + 1 : 0] += C[d][k] * pow((double)A, k / N) * pow((double)B, (d - k) / M); } } vector<double> x = gauss(mat); reverse(x.begin() + 1, x.end()); for (int i = 0; i < size; ++i) { printf("%d%c", int(round(x[i])), i == N * M ? 'n' : ' '); }}int main(int argc, char *argv[]){ build_combinatorial_number(); while (~scanf("%d%d%d%d", &A, &N, &B, &M) && A > 0) { solve(); } return 0;}
