#include #define whlie while #define pb push_back #define eb emplace_back #define fi first #define se second #define rep(i,N) for(int i = 0; i < (N); i++) #define repr(i,N) for(int i = (N) - 1; i >= 0; i--) #define rep1(i,N) for(int i = 1; i <= (N) ; i++) #define repr1(i,N) for(int i = (N) ; i > 0 ; i--) #define each(x,v) for(auto& x : v) #define all(v) (v).begin(),(v).end() #define sz(v) ((int)(v).size()) #define ini(...) int __VA_ARGS__; in(__VA_ARGS__) #define inl(...) ll __VA_ARGS__; in(__VA_ARGS__) #define ins(...) string __VA_ARGS__; in(__VA_ARGS__) using namespace std; void solve(); using ll = long long; using vl = vector; using vi = vector; using vvi = vector< vector >; constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1; struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template ostream& operator <<(ostream& os, const pair &p) { os << p.first << " " << p.second; return os; } template istream& operator >>(istream& is, pair &p) { is >> p.first >> p.second; return is; } template ostream& operator <<(ostream& os, const vector &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os; } template istream& operator >>(istream& is, vector &v) { for(auto &x : v) is >> x; return is; } void in(){} template void in(T &t,U &...u){ cin >> t; in(u...);} void out(){cout << "\n";} template void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);} templatevoid die(T x){out(x); exit(0);} #ifdef NyaanDebug #include "NyaanDebug.h" #define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0) #define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0) #else #define trc(...) #define trca(...) int main(){solve();} #endif //using P = pair; using vp = vector

; constexpr int MOD = /** 1000000007; //*/ 998244353; //////////////// // 素数判定 O( sqrt(N) log log N ) // 0からNに対して素数->1、それ以外->0の配列を返す関数 vector Primes(int N){ vector A(N + 1 , 1); A[0] = A[1] = 0; for(int i = 2; i * i <= N ; i++) if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = 0; return A; } // 因数 O( sqrt(N) log log N ) // 0からNに対して素数->1、それ以外->最小の素数である因数、の配列を返す vector Factors(int N){ vector A(N + 1 , 1); A[0] = A[1] = 0; for(int i = 2; i * i <= N ; i++) if(A[i]==1) for(int j = i << 1 ; j <= N; j += i) A[j] = i; return A; } // オイラーのトーシェント関数 φ(N)=(Nと互いに素なN以下の自然数の個数) vector EulersTotientFunction(int N){ vector ret(N + 1 , 0); for(int i = 0; i <= N ; i++) ret[i] = i; for(int i = 2 ; i <= N ; i++){ if(ret[i] == i) for(int j = i; j <= N; j += i) ret[j] = ret[j] / i * (i - 1); } return ret; } // 約数列挙 O(sqrt(N)) // Nの約数を列挙した配列を返す vector Divisor(long long N){ vector v; for(long long i = 1; i * i <= N ; i++){ if(N % i == 0){ v.push_back(i); if(i * i != N) v.push_back(N / i); } } return v; } // 素因数分解 // 因数をkey、そのべきをvalueとするmapを返す // ex) N=12 -> m={ (2,2) , (3,1) } map PrimeFactors(long long N){ map m; for(long long i=2; i * i <= N; i++) while(N % i == 0) m[i]++ , N /= i; if(N != 1) m[N]++; return m; } // 原始根 modでrが原始根かどうかを調べる bool PrimitiveRoot(long long r , long long mod){ r %= mod; if(r == 0) return false; auto modpow = [](long long a,long long b,long long m)->long long{ a %= m; long long ret = 1; while(b){ if(b & 1) ret = a * ret % m; a = a * a % m; b >>= 1; } return ret; }; map m = PrimeFactors(mod - 1); each(x , m){ if(modpow(r , (mod - 1) / x.fi , mod ) == 1) return false; } return true; } // 拡張ユークリッド ax+by=gcd(a,b)の解 // 返り値 最大公約数 long long extgcd(long long a,long long b, long long &x, long long &y){ if(b == 0){ x = 1; y = 0; return a; } long long d = extgcd(b , a%b , y , x); y -= a / b * x; return d; } // ブール代数ライブラリ // Point. 乗法の単位元は-1 (UNIT & a = aを満たすUNITであるため) struct BA{ unsigned long long x; BA(): x(0){} BA(unsigned long long y):x(y){} BA operator += (const BA &p){ x = x ^ p.x; return (*this); } BA operator *= (const BA &p){ x = x & p.x; return (*this); } BA operator+(const BA &p)const {return BA(*this) += p;} BA operator*(const BA &p)const {return BA(*this) *= p;} bool operator==(const BA &p) const { return x == p.x; } bool operator!=(const BA &p) const { return x != p.x; } friend ostream &operator<<(ostream &os,const BA &p){ return os << p.x; } friend istream &operator>>(istream &is, BA &a){ unsigned int t; is >> t; a = BA(t); return (is); } }; template< int mod > struct NumberTheoreticTransform { vector< int > rev, rts; int base, max_base, root; NumberTheoreticTransform() : 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; } }; void solve(){ ini(P); vi A(P-1) , B(P-1); in(A , B); ll pr = 1; while(PrimitiveRoot(pr , P) == false) pr++; vi p(P-1); p[0] = 1; trc(p); rep1(i , P-2) p[i] = 1LL * p[i-1] * pr % P; vi inv(P); //rep(i,P-1) inv[p[i]] = i ; trc(p); vi s(P-1) , t(P-1); rep(i , P-1){ s[i] = A[p[i] - 1]; t[i] = B[p[i] - 1]; } trc(s,t); NumberTheoreticTransform ntt; auto u = ntt.multiply(s , t); trc(u); for(int i = P-1 ; i < u.size();i++) u[i%(P-1)] = (u[i%(P-1)] + u[i]) % MOD; trc(u); trc(inv); vi ans(P-1); rep(i,P-1) ans[p[i] - 1] = u[i]; out(ans); }