#include using namespace std; using ll = long long; using P = pair; using Vec = vector; #define REP(i, m, n) for(ll i = (m); i < (n); ++i) #define rep(i, n) REP(i, 0, n) template bool chmax(T &a, const T b){if(a < b){a = b; return true;} return false;} template bool chmin(T &a, const T b){if(a > b){a = b; return true;} return false;} constexpr ll LINF = 1e18L+1; constexpr ll MOD = 998244353; const double PI = acos(-1.0); template struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt &operator++() { if((++x) >= mod) x -= mod; return *this; } ModInt operator++(int) { ModInt tmp(*this); operator++(); return tmp; } ModInt &operator--() { if((x += mod - 1) >= mod) x -= mod; return *this; } ModInt operator--(int) { ModInt tmp(*this); operator--(); return tmp; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt res(1), mul(x); while(n > 0) { if(n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using Mint = ModInt; void ntt(vector &a, bool inv){ int N = a.size(); int n = 2, d = N / 2; vector cp(N); while (n <= N) { for (int p = 0; p < d; ++p) { Mint omega = Mint(3).pow((MOD - 1) / n); if (inv) omega = omega.inverse(); Mint pow_omega = 1; for (int i = 0; i < n / 2; ++i) { cp[p + d * i] = a[p + 2 * d * i] + pow_omega * a[p + 2 * d * i + d]; cp[p + d * i + N / 2] = a[p + 2 * d * i] - pow_omega * a[p + 2 * d * i + d]; pow_omega *= omega; } } for (int i = 0; i < N; ++i) a[i] = cp[i]; n <<= 1, d >>= 1; } } void conv(vector &a, vector b){ int n = a.size() + b.size(); int N = 1; while (N <= n) N <<= 1; a.resize(N); b.resize(N); ntt(a, false); ntt(b, false); for (int i = 0; i < N; ++i) { a[i] *= b[i] / N; } ntt(a, true); } vector pn; bool is_prime(ll n){ if(n == 1) return false; for(ll i : pn){ if(i * i > n) return true; if(n % i == 0) return false; } return true; } void init(ll n = 2e5){ if(!pn.empty() && pn.back() >= n) return; pn.push_back(2); for(int i = 3; i < n + 100; ++i) if(is_prime(i)) pn.push_back(i); } vector

prime_factorization(ll n){ init(); vector

res; for(ll i : pn){ ll cnt = 0; while(n % i == 0){ n /= i; cnt++; } if(cnt) res.push_back({i, cnt}); if(n < i * i) break; } if(n != 1) res.push_back({n, 1}); return res; } Vec divisor_enumeration(ll n){ auto v = prime_factorization(n); Vec res, a, b, cp; res.push_back(1); for(auto p : v){ cp.resize(res.size()); copy(res.begin(), res.end(), cp.begin()); a.resize(res.size()); for(int k = 1; k <= p.second; ++k){ ll t = pow(p.first, k); for(int i = 0; i < a.size(); ++i) a[i] = cp[i] * t; merge(res.begin(), res.end(), a.begin(), a.end(), back_inserter(b)); swap(res, b); b.clear(); } } return res; } ll find_root(ll p){ if(p == 3) return 2; auto v = divisor_enumeration(p - 1); for(ll i : v){ unordered_set used; ll t = 1; bool flg = true; for(ll j = 0; j < p - 2; ++j){ (t *= i) % p; if(used.find(t) != used.end()) { flg = false; break; } used.insert(t); } if(flg) return i; } return 0; } int main(void) { ll p; cin >> p; Vec a(p), b(p); rep(i, p - 1) cin >> a[i + 1]; rep(i, p - 1) cin >> b[i + 1]; ll r = find_root(p); cerr << r << endl; ll t = 1; vector u(p), v(p); rep(i, p - 1){ v[i] = a[t]; u[i] = b[t]; (t *= r) %= p; } conv(v, u); t = 1; vector ans(p); rep(i, v.size()){ // cerr << v[i] << endl; ans[t] += v[i]; (t *= r) %= p; } rep(i, p - 1) cout << ans[i + 1] << " "; cout << endl; return 0; }