#include #define rep(i,n) for(int i=0;i<(int)(n);i++) #define rep1(i,n) for(int i=1;i<=(int)(n);i++) #define all(c) c.begin(),c.end() #define pb push_back #define fs first #define sc second #define chmin(x,y) x=min(x,y) #define chmax(x,y) x=max(x,y) using namespace std; template ostream& operator<<(ostream& o,const pair &p){ return o<<"("< ostream& operator<<(ostream& o,const vector &vc){ o<<"{"; for(const T& v:vc) o< using V = vector; template using VV = vector>; constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); } #ifdef LOCAL #define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl #define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {"; \ for(auto v: x) cerr << v << ","; cerr << "}" << endl; #else #define show(x) true #define dump(x) true #endif template struct ModInt{ using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr static uint mod = mod_; uint v; ModInt():v(0){} ModInt(ll _v):v(normS(_v%mod+mod)){} explicit operator bool() const {return v!=0;} static uint normS(const uint &x){return (x [0 , mod-1] static ModInt make(const uint &x){ModInt m; m.v=x; return m;} ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));} ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));} ModInt operator-() const { return make(normS(mod-v)); } ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);} ModInt operator/(const ModInt& b) const { return *this*b.inv();} ModInt& operator+=(const ModInt& b){ return *this=*this+b;} ModInt& operator-=(const ModInt& b){ return *this=*this-b;} ModInt& operator*=(const ModInt& b){ return *this=*this*b;} ModInt& operator/=(const ModInt& b){ return *this=*this/b;} ModInt& operator++(int){ return *this=*this+1;} ModInt& operator--(int){ return *this=*this-1;} ll extgcd(ll a,ll b,ll &x,ll &y) const{ ll p[]={a,1,0},q[]={b,0,1}; while(*q){ ll t=*p/ *q; rep(i,3) swap(p[i]-=t*q[i],q[i]); } if(p[0]<0) rep(i,3) p[i]=-p[i]; x=p[1],y=p[2]; return p[0]; } ModInt inv() const { ll x,y; extgcd(v,mod,x,y); return make(normS(x+mod)); } ModInt pow(ll p) const { if(p<0) return inv().pow(-p); ModInt a = 1; ModInt x = *this; while(p){ if(p&1) a *= x; x *= x; p >>= 1; } return a; } bool operator==(const ModInt& b) const { return v==b.v;} bool operator!=(const ModInt& b) const { return v!=b.v;} friend istream& operator>>(istream &o,ModInt& x){ ll tmp; o>>tmp; x=ModInt(tmp); return o; } friend ostream& operator<<(ostream &o,const ModInt& x){ return o<; int bsr(int x) { return 31 - __builtin_clz(x); } void ntt(bool type, V& c) { const mint G = 3; //primitive root int N = int(c.size()); int s = bsr(N); assert(1 << s == N); V a = c, b(N); rep1(i,s){ int W = 1 << (s - i); mint base = G.pow((mint::mod - 1)>>i); if(type) base = base.inv(); mint now = 1; for(int y = 0; y < N / 2; y += W) { for (int x = 0; x < W; x++) { auto l = a[y << 1 | x]; auto r = now * a[y << 1 | x | W]; b[y | x] = l + r; b[y | x | N >> 1] = l - r; } now *= base; } swap(a, b); } c = a; } V multiply_ntt(const V& a, const V& b) { int A = int(a.size()), B = int(b.size()); if (!A || !B) return {}; int lg = 0; while ((1 << lg) < A + B - 1) lg++; int N = 1 << lg; V ac(N), bc(N); for (int i = 0; i < A; i++) ac[i] = a[i]; for (int i = 0; i < B; i++) bc[i] = b[i]; ntt(false, ac); ntt(false, bc); for (int i = 0; i < N; i++) { ac[i] *= bc[i]; } ntt(true, ac); V c(A + B - 1); mint iN = mint(N).inv(); for (int i = 0; i < A + B - 1; i++) { c[i] = ac[i] * iN; } return c; } int main(){ cin.tie(0); ios::sync_with_stdio(false); //DON'T USE scanf/printf/puts !! cout << fixed << setprecision(20); ll p; cin >> p; V a(p); rep1(i,p-1) cin >> a[i]; V b(p); rep1(i,p-1) cin >> b[i]; ll g = 1; for(int i=2;i lg(p),gl(p); { ll x = 1; rep(t,p-1){ lg[x] = t; gl[t] = x; x *= g; x %= p; } } V A(p-1),B(p-1); rep1(x,p-1){ A[lg[x]] = a[x]; B[lg[x]] = b[x]; } show(A); show(B); auto C = multiply_ntt(A,B); V c(p); rep(i,C.size()) c[gl[i%(p-1)]] += C[i]; rep1(i,p-1) cout << c[i] << " "; cout << endl; }