// warm heart, wagging tail,and a smile just for you! // ███████████ // ███╬╬╬╬╬╬╬╬╬╬███ // ███╬╬╬╬╬████╬╬╬╬╬╬███ // ███████████ ██╬╬╬╬╬████╬╬████╬╬╬╬╬██ // █████████╬╬╬╬╬████████████╬╬╬╬╬██╬╬╬╬╬╬███╬╬╬╬╬██ // ████████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬██╬╬╬╬╬╬╬██ // ████╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬╬╬╬╬╬██ // ███╬╬╬█╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬███╬╬╬╬╬╬╬█████ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬████████╬╬╬╬╬██ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬╬╬╬╬███ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬██ // ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬████ // █████████████╬╬╬╬╬╬╬╬██╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬██████ // ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬██████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████╬╬╬╬╬╬╬███████████╬╬╬╬╬╬╬╬██╬╬╬██╬╬╬██ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬█╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬██ // ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬▓▓▓▓▓▓╬╬╬████╬╬████╬╬╬╬╬╬╬▓▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬███ // ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████▓▓▓▓▓▓▓╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬█████ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████████ // ███╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██ // ██████████████ ████╬╬╬╬╬╬███████████████████████████╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████ // ███████ █████ ███████████████████ // #include "bits/stdc++.h" using namespace std; #define INF (1<<30) #define LINF (1LL<<60) #define fs first #define sc second #define int long long #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define FOR2(i,a,b) for(int i=(a);i<=(b);++i) #define RFOR(i,a,b) for(int i = (b-1);i>=(a);--i) #define RFOR2(i,a,b) for(int i = (b);i>=(a);--i) #define REP(i,n) FOR(i,0,(n)) #define REP2(i,n) FOR2(i,0,(n)) #define RREP(i,n) RFOR(i,0,(n)) #define RREP2(i,n) RFOR2(i,0,(n)) #define ITR(itr,mp) for(auto itr = (mp).begin(); itr != (mp).end(); ++itr) #define RITR(itr,mp) for(auto itr = (mp).rbegin(); itr != (mp).rend(); ++itr) #define range(i,a,b) ((a)<=(i) && (i)<(b)) #define debug(x) cout << #x << " = " << (x) << endl #define SP << " " << template inline bool chmin(T1 &a,T2 b){if(a>b) {a=b; return true;} else return false;} template inline bool chmax(T1 &a,T2 b){if(a P; typedef tuple T; vector MODS = { 1000000007, 998244353 }; // 実行時に決まる template struct Fp { long long val; int MOD = MODS[IND]; constexpr Fp(long long v = 0) noexcept : val(v % MODS[IND]) { if (val < 0) val += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp& x) noexcept { return os << x.val; } friend constexpr istream& operator >> (istream &is, Fp& x) noexcept { return is >> x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; using mint = Fp<1>; // MODを変える場合は値を変更 typedef vector vec; typedef vector> mat; vec fact,inv; void init(int n){ fact.assign(n+1,1); inv.assign(n+1,1); REP(i,n) fact[i+1] = fact[i]*(i+1), inv[i+1] /= fact[i+1]; } mint cmb(int n, int r){ if(n < r) return 0; return fact[n]*inv[r]*inv[n-r]; } int get_root(int p) { // pの原子根を求める for(int i=2;i S; int x=1,j; while(1) { if(S.size()==p-1) return i; if(S.count(x)) break; S.insert(x); x=x*i%p; } } assert(0); } constexpr int bmds(int x){ if(x==0) return 1012924417; if(x==1) return 924844033; if(x==2) return 998244353; if(x==3) return 897581057; if(x==4) return 645922817; } constexpr int brts(int x){ if(x==0) return 5; if(x==1) return 5; if(x==2) return 3; if(x==3) return 3; if(x==4) return 3; } template struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); inline int add(int a,int b){ a+=b; if(a>=md) a-=md; return a; } inline int mul(int a,int b){ return 1LL*a*b%md; } inline int pow(int a,int b){ int res=1; while(b){ if(b&1) res=mul(res,a); a=mul(a,a); b>>=1; } return res; } inline int inv(int x){ return pow(x,md-2); } vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &a,bool f,int n=-1){ if(n==-1) n=a.size(); assert((n&(n-1))==0); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(a[i],a[j]); } for(int i=1;i multiply(vector &a,vector &b){ int need=a.size()+b.size()-1; int sz=1; while(sz f(sz),g(sz); for(int i=0;i<(int)a.size();i++) f[i]=a[i]; for(int i=0;i<(int)b.size();i++) g[i]=b[i]; ntt(f,0);ntt(g,0); for(int i=0;i> P; vector a(P); REP(i,P-1) cin >> a[i+1]; vector b(P); REP(i,P-1) cin >> b[i+1]; if(P==2){ cout << (mint)a[1]*b[1] << endl; return; } int g = get_root(P); vector x(P-1,0),y(P-1,0); // x[i] = a[g^i] int v = 1; REP(i,P-1){ x[i] = a[v]; y[i] = b[v]; v *= g; v %= P; } NTT<2> ntt; auto z = ntt.multiply(x,y); // c[g^i] = sum(j+k==i){a[g^j]*b[g^k]} -> z[i] = sum(j+k==i){x[j]*y[k]} vec ans(P); v = 1; REP(i,z.size()){ ans[v] += z[i]; v *= g; v %= P; } REP(i,P-1) cout << ans[i+1] << " "; cout << endl; } signed main(){ ios::sync_with_stdio(false); cin.tie(0); int T = 1; // cin >> T; while(T--) solve(); return 0; }