結果

問題 No.931 Multiplicative Convolution
ユーザー maroon_kuri
提出日時 2019-11-22 22:14:15
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 145 ms / 2,000 ms
コード長 7,802 bytes
コンパイル時間 1,914 ms
コンパイル使用メモリ 180,128 KB
実行使用メモリ 63,208 KB
最終ジャッジ日時 2024-10-11 03:54:57
合計ジャッジ時間 5,004 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
    return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
    os<<"{";
    for(auto e:v)os<<e<<",";
    return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
    os<<t<<" ";
    dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,"Line:",__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
    if(i)os<<",";
    os<<get<i>(t);
    print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
    os<<"{";
    print_tuple<0,tuple<Args...>,Args...>(os,t);
    return os<<"}";
}
void print(ll x,int suc=1){
    cout<<x;
    if(suc==1)
        cout<<"\n";
    if(suc==2)
        cout<<" ";
}
ll read(){
    ll i;
    cin>>i;
    return i;
}
vi readvi(int n,int off=0){
    vi v(n);
    rep(i,n)v[i]=read()+off;
    return v;
}
template<class T>
void print(const vector<T>&v,int suc=1){
    rep(i,v.size())
        print(v[i],i==int(v.size())-1?suc:2);
}
string readString(){
    string s;
    cin>>s;
    return s;
}
template<class T>
T sq(const T& t){
    return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
    #ifdef CAPITAL
    cout<<"YES"<<endl;
    #else
    cout<<"Yes"<<endl;
    #endif
    if(ex)exit(0);
}
void no(bool ex=true){
    #ifdef CAPITAL
    cout<<"NO"<<endl;
    #else
    cout<<"No"<<endl;
    #endif
    if(ex)exit(0);
}
constexpr ll ten(int n){
    return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
    return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
    return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
    return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
    return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
    return __builtin_popcount(t);
}
int popcount(ll t){
    return __builtin_popcountll(t);
}
bool ispow2(int i){
    return i&&(i&-i)==i;
}
int mask(int i){
    return (int(1)<<i)-1;
}
bool inc(int a,int b,int c){
    return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
    sort(all(v));
    v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
    #ifdef LOCAL
    static mt19937_64 gen;
    #else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
    return lower_bound(all(v),a)-v.bg;
}
using uint=unsigned;
using ull=unsigned long long;
//initfact();
const uint mod=998244353;
//const uint mod=1000000007;
//uint mod=1;
struct mint{
    uint v;
    mint(ll vv=0){s(vv%mod+mod);}
    mint& s(uint vv){
        v=vv<mod?vv:vv-mod;
        return *this;
    }
    mint operator-()const{return mint()-*this;}
    mint& operator+=(const mint&rhs){return s(v+rhs.v);}
    mint&operator-=(const mint&rhs){return s(v+mod-rhs.v);}
    mint&operator*=(const mint&rhs){
        v=ull(v)*rhs.v%mod;
        return *this;
    }
    mint&operator/=(const mint&rhs){return *this*=rhs.inv();}
    mint operator+(const mint&rhs)const{return mint(*this)+=rhs;}
    mint operator-(const mint&rhs)const{return mint(*this)-=rhs;}
    mint operator*(const mint&rhs)const{return mint(*this)*=rhs;}
    mint operator/(const mint&rhs)const{return mint(*this)/=rhs;}
    mint pow(int n)const{
        mint res(1),x(*this);
        while(n){
            if(n&1)res*=x;
            x*=x;
            n>>=1;
        }
        return res;
    }
    mint inv()const{return pow(mod-2);}
    /*mint inv()const{
        int x,y;
        int g=extgcd(v,mod,x,y);
        assert(g==1);
        if(x<0)x+=mod;
        return mint(x);
    }*/
    friend ostream& operator<<(ostream&os,const mint&m){
        return os<<m.v;
    }
    bool operator<(const mint&r)const{return v<r.v;}
    bool operator==(const mint&r)const{return v==r.v;}
};
const int vmax=(1<<21)+10;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
    fact[0]=1;
    rng(i,1,vmax){
        fact[i]=fact[i-1]*i;
    }
    finv[vmax-1]=fact[vmax-1].inv();
    for(int i=vmax-2;i>=0;i--){
        finv[i]=finv[i+1]*(i+1);
    }
    for(int i=vmax-1;i>=1;i--){
        invs[i]=finv[i]*fact[i-1];
    }
}
mint choose(int n,int k){
    return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
    return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
    return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}
#define USE_FMT
//998244353
const mint prim_root=3;
/*
//in-place fft
//size of input must be a power of 2
void inplace_fmt(vector<mint>&f,const bool inv){
    const int n=f.size();
    const mint root=inv?prim_root.inv():prim_root;
    vc<mint> g(n);
    for(int b=n/2;b>=1;b/=2){
        mint w=root.pow((mint::base-1)/(n/b)),p=1;
        for(int i=0;i<n;i+=b*2){
            rep(j,b){
                f[i+j+b]*=p;
                g[i/2+j]=f[i+j]+f[i+b+j];
                g[n/2+i/2+j]=f[i+j]-f[i+b+j];
            }
            p*=w;
        }
        swap(f,g);
    }
    if(inv)rep(i,n)
        f[i]*=inv[n];
}*/
static const int LG=21;
mint roots[1<<(LG+1)],iroots[1<<(LG+1)];
struct PrepareRoots{
    PrepareRoots(){
        rep(w,LG+1){
            const int s=(1<<w)-1;
            const mint g=prim_root.pow((mod-1)/(1<<w)),ig=g.inv();
            mint p=1,ip=1;
            rep(i,1<<w){
                roots[s+i]=p;p*=g;
                iroots[s+i]=ip;ip*=ig;
            }
        }
    }
} PrepareRootsDummy;
void broken_fmt(vc<mint>&f){
    const int n=f.size();
    for(int b=n/2;b>=1;b/=2){
        for(int i=0;i<n;i+=b*2){
            rep(j,b){
                mint tmp=f[i+j]-f[i+j+b];
                f[i+j]+=f[i+j+b];
                f[i+j+b]=tmp*roots[b*2-1+j];
            }
        }
    }
}
void broken_ifmt(vc<mint>&f){
    const int n=f.size();
    for(int b=1;b<=n/2;b*=2){
        for(int i=0;i<n;i+=b*2){
            rep(j,b){
                f[i+j+b]*=iroots[b*2-1+j];
                mint tmp=f[i+j]-f[i+j+b];
                f[i+j]+=f[i+j+b];
                f[i+j+b]=tmp;
            }
        }
    }
    rep(i,n)
        f[i]*=invs[n];
}
void inplace_fmt(vector<mint>&f,const bool i){
    if(!i)broken_fmt(f);
    else broken_ifmt(f);
}
vc<mint> multiply(vc<mint> x,vc<mint> y,bool same=false){
    dmp(x);
    dmp(y);
    int n=x.size()+y.size()-1;
    int s=1;
    while(s<n)s*=2;
    x.resize(s);inplace_fmt(x,false);
    if(!same){
        y.resize(s);inplace_fmt(y,false);
    }else
        y=x;
    rep(i,s)
        x[i]*=y[i];
    inplace_fmt(x,true);x.resize(n);
    return x;
}
template<class t>
t pow_mod(t x,t n,t m){
    t r=1;
    while(n){
        if(n&1)r=(r*x)%m;
        x=(x*x)%m;
        n>>=1;
    }
    return r;
}
bool CheckPrimitiveRoot(int r,int p){
    if(!r)return false;
    int x=p-1;
    for(int i=2;i*i<=x;i++){
        if(x%i==0){
            int w=pow_mod<int>(r,(p-1)/i,p);
            if(w==1)return false;
            while(x%i==0)
                x/=i;
        }
    }
    return true;
}
signed main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout<<fixed<<setprecision(20);
    
    initfact();
    
    int p;cin>>p;
    int w=1;
    rng(i,2,p){
        if(CheckPrimitiveRoot(i,p)){
            w=i;
            break;
        }
    }
    dmp(w);
    
    auto waf=[&](){
        vi a=readvi(p-1);
        vc<mint> res(p-1);
        int x=1;
        rep(i,p-1){
            res[i]=a[x-1];
            x=(x*w)%p;
        }
        return res;
    };
    
    auto z=multiply(waf(),waf());
    
    vc<mint> ans(p-1);
    int x=1;
    rep(i,z.size()){
        ans[x-1]+=z[i];
        x=(x*w)%p;
    }
    
    rep(i,ans.size()){
        cout<<ans[i]<<(i<(int)ans.size()-1?" ":"\n");
    }
}
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