#include #define rep(i,n) for(int i = 0; i < (n); i++) using namespace std; typedef long long ll; ll modpow(ll a,ll b,ll mod){ ll ans = 1; a %= mod; while(b){ if(b&1) ans = ans * a % mod; a = a * a % mod; b >>= 1; } return ans; } int get_root(int p) { vector ds; for(int i = 1; i * i <= p - 1; i++){ if((p - 1) % i == 0){ ds.push_back(i); if(i * i != p - 1) ds.push_back((p - 1) / i); } } sort(ds.begin(), ds.end()); ds.pop_back(); for(int i = 1; i <= p - 1; i++){ for(auto &d : ds) if(modpow(i, d, p) == 1) goto fail; return i; fail:; } return -1; } template< int mod > struct Fp { int x; Fp() : x(0) {} Fp(int64_t y) : x(y >= 0 ? y % mod : (mod + y % mod) % mod) {} Fp &operator+=(const Fp &p) { if((x += p.x) >= mod) x -= mod; return *this; } Fp &operator-=(const Fp &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } Fp &operator*=(const Fp &p) { x = (int)(1LL * x * p.x % mod); return *this; } Fp &operator/=(const Fp &p) { *this *= p.inv(); return *this; } Fp operator-() const { return Fp(-x); } Fp operator+(const Fp &p) const { return Fp(*this) += p; } Fp operator-(const Fp &p) const { return Fp(*this) -= p; } Fp operator*(const Fp &p) const { return Fp(*this) *= p; } Fp operator/(const Fp &p) const { return Fp(*this) /= p; } bool operator==(const Fp &p) const { return x == p.x; } bool operator!=(const Fp &p) const { return x != p.x; } Fp inv() 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 Fp(u); } Fp pow(int64_t n) const { Fp ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const Fp &p) { return os << p.x; } friend istream &operator>>(istream &is, Fp &a) { int64_t t; is >> t; a = Fp< mod > (t); return (is); } static int get_mod() { return mod; } }; using mint = Fp<998244353>; template< int mod > struct NTT { vector< int > rev, rts; int base, max_base, root; NTT() : base(1), rev{0, 1}, rts{0, 1} { assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(mod_pow(root, (mod - 1) >> 1) == 1) ++root; assert(mod_pow(root, mod - 1) == 1); root = mod_pow(root, (mod - 1) >> max_base); } inline int mod_pow(int x, int n) { int ret = 1; while(n > 0) { if(n & 1) ret = mul(ret, x); x = mul(x, x); n >>= 1; } return ret; } inline int inverse(int x) { return mod_pow(x, mod - 2); } inline unsigned add(unsigned x, unsigned y) { x += y; if(x >= mod) x -= mod; return x; } inline unsigned mul(unsigned a, unsigned b) { return 1ull * a * b % (unsigned long long) mod; } void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } assert(nbase <= max_base); while(base < nbase) { int z = mod_pow(root, 1 << (max_base - 1 - base)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; rts[(i << 1) + 1] = mul(rts[i], z); } ++base; } } void ntt(vector< int > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { int z = mul(a[i + j + k], rts[j + k]); a[i + j + k] = add(a[i + j], mod - z); a[i + j] = add(a[i + j], z); } } } } vector< int > multiply(vector< int > a, vector< int > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); int inv_sz = inverse(sz); for(int i = 0; i < sz; i++) { a[i] = mul(a[i], mul(b[i], inv_sz)); } reverse(a.begin() + 1, a.end()); ntt(a); a.resize(need); return a; } }; int main(){ cin.tie(0); ios::sync_with_stdio(0); int P; cin >> P; vector A(P), B(P); for(int i = 1; i < P; i++) cin >> A[i]; for(int i = 1; i < P; i++) cin >> B[i]; int g = get_root(P); vector va(P - 1), vb(P - 1); int x = 1; rep(i,P-1){ va[i] = A[x]; vb[i] = B[x]; x = (ll)x * g % P; } NTT<998244353> ntt; auto vc = ntt.multiply(va, vb); rep(i,vc.size()) if(i >= P - 1) { vc[i - (P - 1)] += vc[i]; } vector ans(P); x = 1; rep(i,P-1){ ans[x] = vc[i]; x = (ll)x * g % P; } for(int i = 1; i < P; i++){ if(i > 1) cout << " "; cout << ans[i]; }cout << endl; }