// correct #include #include #include #include #include using mint = atcoder::modint; mint inv2, inv3, inv4; mint H(int i, int d) { static std::vector pow_inv4{ 1 }; for (int siz = pow_inv4.size(); siz <= i; ++siz) { mint nxt_pow = pow_inv4.back() * inv4; pow_inv4.push_back(nxt_pow); } return i * inv3 - (inv3 + d) * (1 - pow_inv4[i]) * inv3; } mint T(int i, int d) { return H(i, d); } std::vector solve(int n) { constexpr int OFFSET = 1; // max x s.t. x+(x-1) <= i constexpr auto max_x = [](int i) -> int { return (i + 1) / 2; }; std::vector P(max_x(0) + 1, std::vector(3)); P[0][0 + OFFSET] = 1; std::vector R(n, 1); for (int i = 0; i < n; ++i) { std::vector nxt_P(max_x(i + 1) + 1, std::vector(3)); for (int x = 0; x <= max_x(i); ++x) for (int d = -1; d <= 1; ++d) { const int z = x + d, y = i - x - z; const mint p = P[x][d + OFFSET]; if (p == 0) { // skip invalid states (e.g. min(x,y,z)<0) continue; } if (d == -1) { // head R[i] += p * inv2 * y; nxt_P[x][-1 + OFFSET] += p * inv2; // tail R[i] += p * inv2 * (n - 1 - T(n - 1 - i, 0)); nxt_P[x][0 + OFFSET] += p * inv2; } else if (d == 1) { // nop R[i] += p * (x + y + H(n - 1 - i, 0)); nxt_P[x + 1][0 + OFFSET] += p; } else { // nop R[i] += p * inv2 * (x + y + H(n - 1 - i, -1)); nxt_P[x + 1][-1 + OFFSET] += p * inv2; // head R[i] += p * inv4 * y; nxt_P[x][0 + OFFSET] += p * inv4; // tail R[i] += p * inv4 * (n - 1 - T(n - 1 - i, 1)); nxt_P[x][1 + OFFSET] += p * inv4; } } P.swap(nxt_P); } return R; } int main() { int n, p; std::cin >> n >> p; mint::set_mod(p); inv2 = mint(1) / 2; inv3 = mint(1) / 3; inv4 = mint(1) / 4; std::vector R = solve(n); for (int i = 0; i < n; ++i) { if (i != 0) std::cout << ' '; std::cout << R[i].val(); } std::cout << std::endl; }