#937885 (C++17) No.2579 Dice Sum Infinity (制約変更版)

• 問題: No.2579 Dice Sum Infinity (制約変更版)
• ユーザー: tko919
• 提出日時: 2023-12-11 07:38:47
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 783 ms / 6,000 ms
• コード長: 20,844 bytes
• コンパイル時間: 5,321 ms
• コンパイル使用メモリ: 238,204 KB
• 実行使用メモリ: 6,676 KB
• 最終ジャッジ日時: 2023-12-11 07:38:58
• 合計ジャッジ時間: 10,527 ms
• ジャッジサーバーID （参考情報）: judge15 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,676 KB
testcase_01	AC	1 ms; 6,676 KB
testcase_02	AC	200 ms; 6,676 KB
testcase_03	AC	235 ms; 6,676 KB
testcase_04	AC	737 ms; 6,676 KB
testcase_05	AC	721 ms; 6,676 KB
testcase_06	AC	783 ms; 6,676 KB
testcase_07	AC	382 ms; 6,676 KB
testcase_08	AC	504 ms; 6,676 KB

ソースコード

#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin())
#define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin())

using ll=long long int;
using ull=unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
template<typename T,typename U>T ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>T floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);}
template<typename T>int popcnt(T x){return __builtin_popcountll(x);}
template<typename T>int topbit(T x){return (x==0?-1:63-__builtin_clzll(x));}
template<typename T>int lowbit(T x){return (x==0?-1:__builtin_ctzll(x));}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO{
    static constexpr int L=1<<16;
    char rdbuf[L];
    int rdLeft=0,rdRight=0;
    inline void reload(){
        int len=rdRight-rdLeft;
        memmove(rdbuf,rdbuf+rdLeft,len);
        rdLeft=0,rdRight=len;
        rdRight+=fread(rdbuf+len,1,L-len,stdin);
    }
    inline bool skip(){
        for(;;){
            while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;
            if(rdLeft==rdRight){
                reload();
                if(rdLeft==rdRight)return false;
            }
            else break;
        }
        return true;
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__int128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));
        }
        return true;
    }
    inline bool _read(__uint128_t& x){
        if(!skip())return false;
        if(rdLeft+40>=rdRight)reload();
        x=0;
        while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        return true;
    }
    template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){
        if(!skip())return false;
        if(rdLeft+20>=rdRight)reload();
        bool neg=false;
        if(rdbuf[rdLeft]=='-'){
            neg=true;
            rdLeft++;
        }
        x=0;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x=x*10+(rdbuf[rdLeft++]^48);
        }
        if(rdbuf[rdLeft]!='.')return true;
        rdLeft++;
        T base=.1;
        while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){
            x+=base*(rdbuf[rdLeft++]^48);
            base*=.1;
        }
        if(neg)x=-x;
        return true;
    }
    inline bool _read(char& x){
        if(!skip())return false;
        if(rdLeft+1>=rdRight)reload();
        x=rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string& x){
        if(!skip())return false;
        for(;;){
            int pos=rdLeft;
            while(pos<rdRight and rdbuf[pos]>' ')pos++;
            x.append(rdbuf+rdLeft,pos-rdLeft);
            if(rdLeft==pos)break;
            rdLeft=pos;
            if(rdLeft==rdRight)reload();
            else break;
        }
        return true;
    }
    template<typename T>inline bool _read(vector<T>& v){
        for(auto& x:v){
            if(!_read(x))return false;
        }
        return true;
    }

    char wtbuf[L],tmp[50];
    int wtRight=0;
    inline void flush(){
        fwrite(wtbuf,1,wtRight,stdout);
        wtRight=0;
    }
    inline void _write(const char& x){
        if(wtRight>L-32)flush();
        wtbuf[wtRight++]=x;
    }
    inline void _write(const string& x){
        for(auto& c:x)_write(c);
    }
    template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){
        if(wtRight>L-32)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2: _write("32768"); return;
                case 4: _write("2147483648"); return;
                case 8: _write("9223372036854775808"); return;
                }
            }
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__int128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        else if(x<0){
            _write('-');
            x=-x;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    inline void _write(__uint128_t x){
        if(wtRight>L-40)flush();
        if(x==0){
            _write('0');
            return;
        }
        int pos=0;
        while(x!=0){
            tmp[pos++]=char((x%10)|48);
            x/=10;
        }
        rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];
        wtRight+=pos;
    }
    template<typename T>inline void _write(const vector<T>& v){
        rep(i,0,v.size()){
            if(i)_write(' ');
            _write(v[i]);
        }
    }
public:
    FastIO(){}
    ~FastIO(){flush();}
    inline void read(){}
    template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){
        assert(_read(head));
        read(tail...); 
    }
    template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}
    template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){
        if(space)_write(' ');
        _write(head);
        write<ln,true>(tail...); 
    }
};

/**
 * @brief Fast IO
 */
#line 3 "sol.cpp"

#line 2 "library/Math/modint.hpp"

template<int mod=1000000007>struct fp {
    int v;
    static constexpr int get_mod(){return mod;}
    int inv() const{
        int tmp,a=v,b=mod,x=1,y=0;
        while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);
        if(x<0){x+=mod;} return x;
    }
    fp(ll x=0){init(x%mod+mod);}
    fp& init(ll x){v=(x<mod?x:x-mod); return *this;}
    fp operator-()const{return fp()-*this;}
    fp pow(ll t){assert(t>=0); fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}
    fp& operator+=(const fp& x){return init(v+x.v);}
    fp& operator-=(const fp& x){return init(v+mod-x.v);}
    fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}
    fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}
    fp operator+(const fp& x)const{return fp(*this)+=x;}
    fp operator-(const fp& x)const{return fp(*this)-=x;}
    fp operator*(const fp& x)const{return fp(*this)*=x;}
    fp operator/(const fp& x)const{return fp(*this)/=x;}
    bool operator==(const fp& x)const{return v==x.v;}
    bool operator!=(const fp& x)const{return v!=x.v;}
    friend istream& operator>>(istream& is,fp& x){return is>>x.v;}
    friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}
};

template<typename T>T Inv(ll n){
    static const int md=T::get_mod();
    static vector<T> buf({0,1});
    assert(n>0);
    n%=md;
    while(SZ(buf)<=n){
        int k=SZ(buf),q=(md+k-1)/k;
        buf.push_back(buf[k*q-md]*q);
    }
    return buf[n];
}

template<typename T>T Fact(ll n,bool inv=0){
    static const int md=T::get_mod();
    static vector<T> buf({1,1}),ibuf({1,1});
    assert(n>=0 and n<md);
    while(SZ(buf)<=n){
        buf.push_back(buf.back()*SZ(buf));
        ibuf.push_back(ibuf.back()*Inv<T>(SZ(ibuf)));
    }
    return inv?ibuf[n]:buf[n];
}

template<typename T>T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return Fact<T>(n,inv)*Fact<T>(n-r,inv^1);}
template<typename T>T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return Fact<T>(n,inv)*Fact<T>(r,inv^1)*Fact<T>(n-r,inv^1);}
template<typename T>T nHr(int n,int r,bool inv=0){return nCr<T>(n+r-1,r,inv);}

/**
 * @brief Modint
 */
#line 2 "library/Convolution/ntt.hpp"

template<typename T,unsigned p=3>struct NTT{
    vector<T> rt,irt;
    NTT(int lg=21){
        unsigned m=T::get_mod()-1; T prt=p;
        rt.resize(lg); irt.resize(lg);
        rep(k,0,lg){
            rt[k]=-prt.pow(m>>(k+2));
            irt[k]=rt[k].inv();
        }
    }
    void ntt(vector<T>& f,bool inv=0){
        int n=f.size();
        if(inv){
            for(int m=1;m<n;m<<=1){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j];
                        f[i]=x+y; f[j]=(x-y)*w;
                    } w*=irt[__builtin_ctz(++t)];
                }
             } T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
        }else{
            for(int m=n;m>>=1;){ T w=1;
                for(int s=0,t=0;s<n;s+=m*2){
                    for(int i=s,j=s+m;i<s+m;i++,j++){
                        auto x=f[i],y=f[j]*w;
                        f[i]=x+y; f[j]=x-y;
                    } w*=rt[__builtin_ctz(++t)];
                }
            }
         }
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m); rep(i,0,b.size())c[i]=b[i];
            ntt(c); rep(i,0,m)res[i]*=c[i];
        } ntt(res,1); res.resize(n); return res;
    }
};

/**
 * @brief Number Theoretic Transform
 */
#line 2 "library/FPS/fps.hpp"

template<typename T>struct Poly:vector<T>{
    Poly(int n=0){this->assign(n,T());}
    Poly(const initializer_list<T> f):vector<T>::vector(f){}
    Poly(const vector<T>& f){this->assign(ALL(f));}
    T eval(const T& x){
        T res;
        for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);
        return res;
    }
    Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}
    void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}
    Poly operator>>(int sz)const{
        if((int)this->size()<=sz)return {};
        Poly ret(*this);
        ret.erase(ret.begin(),ret.begin()+sz);
        return ret;
    }
    Poly operator<<(int sz)const{
        Poly ret(*this);
        ret.insert(ret.begin(),sz,T(0));
        return ret;
    }
    vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0)const{
        if(a.empty() or b.empty())return vector<T>();
        int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);
        vector<T> res(m);
        rep(i,0,a.size())res[i]=a[i];
        NTT(res,0);
        if(same)rep(i,0,m)res[i]*=res[i];
        else{
            vector<T> c(m);
            rep(i,0,b.size())c[i]=b[i];
            NTT(c,0);
            rep(i,0,m)res[i]*=c[i];
        }
        NTT(res,1);
        res.resize(n);
        return res;
    }
    Poly square()const{return Poly(mult(*this,*this,1));}
    Poly operator-()const{return Poly()-*this;}
    Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
    Poly operator+(const T& g)const{return Poly(*this)+=g;}
    Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
    Poly operator-(const T& g)const{return Poly(*this)-=g;}
    Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
    Poly operator*(const T& g)const{return Poly(*this)*=g;}
    Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
    Poly operator/(const T& g)const{return Poly(*this)/=g;}
    Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
    pair<Poly,Poly> divmod(const Poly& g)const{
        Poly q=*this/g,r=*this-g*q;
        r.shrink();
        return {q,r};
    }
    Poly& operator+=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;
    }
    Poly& operator+=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]+=g; return *this;
    }
    Poly& operator-=(const Poly& g){
        if(g.size()>this->size())this->resize(g.size());
        rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;
    }
    Poly& operator-=(const T& g){
        if(this->empty())this->push_back(0);
        (*this)[0]-=g; return *this;
    }
    Poly& operator*=(const Poly& g){
        *this=mult(*this,g,0);
        return *this;
    }
    Poly& operator*=(const T& g){
        rep(i,0,this->size())(*this)[i]*=g;
        return *this;
    }
    Poly& operator/=(const Poly& g){
        if(g.size()>this->size()){
            this->clear(); return *this;
        }
        Poly g2=g;
        reverse(ALL(*this));
        reverse(ALL(g2));
        int n=this->size()-g2.size()+1;
        this->resize(n); g2.resize(n);
        *this*=g2.inv(); this->resize(n); 
        reverse(ALL(*this));
        shrink();
        return *this;
    }
    Poly& operator/=(const T& g){
        rep(i,0,this->size())(*this)[i]/=g;
        return *this;
    }
    Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}
    Poly diff()const{
        Poly res(this->size()-1);
        rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);
        return res;
    }
    Poly inte()const{
        Poly res(this->size()+1);
        for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;
        return res;
    }
    Poly log()const{
        assert(this->front()==1); const int n=this->size();
        Poly res=diff()*inv(); res=res.inte(); 
        res.resize(n); return res;
    }
    Poly shift(const int& c)const{
        const int n=this->size();
        Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;
        vector<T> fact(n,1);
        rep(i,0,n){
            if(i)fact[i]=fact[i-1]*i;
            res[i]*=fact[i];
        }
        res=res.rev();
        res*=g;
        res.resize(n);
        res=res.rev();
        rep(i,0,n)res[i]/=fact[i];
        return res;
    }
    Poly inv()const{
        const int n=this->size();
        Poly res(1); res.front()=T(1)/this->front();
        for(int k=1;k<n;k<<=1){
            Poly f(k*2),g(k*2);
            rep(i,0,min(n,k*2))f[i]=(*this)[i];
            rep(i,0,k)g[i]=res[i];
            NTT(f,0);
            NTT(g,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k){f[i]=0; f[i+k]=-f[i+k];}
            NTT(f,0);
            rep(i,0,k*2)f[i]*=g[i];
            NTT(f,1);
            rep(i,0,k)f[i]=res[i];
            swap(res,f);
        } res.resize(n); return res;
    }
    Poly exp()const{
        const int n=this->size();
        if(n==1)return Poly({T(1)});
        Poly b(2),c(1),z1,z2(2);
        b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1];
        for(int k=2;k<n;k<<=1){
            Poly y=b;
            y.resize(k*2);
            NTT(y,0);
            z1=z2;
            Poly z(k);
            rep(i,0,k)z[i]=y[i]*z1[i];
            NTT(z,1);
            rep(i,0,k>>1)z[i]=0;
            NTT(z,0);
            rep(i,0,k)z[i]*=-z1[i];
            NTT(z,1);
            c.insert(c.end(),z.begin()+(k>>1),z.end());
            z2=c;
            z2.resize(k*2);
            NTT(z2,0);
            Poly x=*this;
            x.resize(k);
            x=x.diff();x.resize(k);
            NTT(x,0);
            rep(i,0,k)x[i]*=y[i];
            NTT(x,1);
            Poly bb=b.diff();
            rep(i,0,k-1)x[i]-=bb[i];
            x.resize(k*2);
            rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;}
            NTT(x,0);
            rep(i,0,k*2)x[i]*=z2[i];
            NTT(x,1);
            x.pop_back();
            x=x.inte();
            rep(i,k,min(n,k*2))x[i]+=(*this)[i];
            rep(i,0,k)x[i]=0;
            NTT(x,0);
            rep(i,0,k*2)x[i]*=y[i];
            NTT(x,1);
            b.insert(b.end(),x.begin()+k,x.end());
        } b.resize(n); return b;
    }
    Poly pow(ll t){
        if(t==0){
            Poly res(this->size()); res[0]=1;
            return res;
        }
        int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;
        Poly res(n); if(__int128_t(t)*k>=n)return res;
        n-=t*k; Poly g(n); T c=(*this)[k],ic=c.inv();
        rep(i,0,n)g[i]=(*this)[i+k]*ic;
        g=g.log(); for(auto& x:g)x*=t; g=g.exp();
        c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;
    }
    void NTT(vector<T>& a,bool inv)const;
};

/**
 * @brief Formal Power Series (NTT-friendly mod)
 */
#line 7 "sol.cpp"
using Fp=fp<998244353>;
NTT<Fp,3> ntt;
template<>void Poly<Fp>::NTT(vector<Fp>& v,bool inv)const{return ntt.ntt(v,inv);}

#line 2 "library/FPS/nthterm.hpp"

template<typename T>T nth(Poly<T> p,Poly<T> q,ll n){
    while(n){
        Poly<T> base(q),np,nq;
        for(int i=1;i<(int)q.size();i+=2)base[i]=-base[i];
        p*=base; q*=base;
        for(int i=n&1;i<(int)p.size();i+=2)np.emplace_back(p[i]);
        for(int i=0;i<(int)q.size();i+=2)nq.emplace_back(q[i]);
        swap(p,np); swap(q,nq);
        n>>=1;
    }
    return p[0]/q[0];
}

/**
 * @brief Bostan-Mori Algorithm
 */
#line 2 "library/FPS/halfgcd.hpp"

namespace HalfGCD{
    template<typename T>using P=array<T,2>;
    template<typename T>using Mat=array<T,4>;
    template<typename T>P<T> operator*(const Mat<T>& a,const P<T>& b){
        P<T> ret={a[0]*b[0]+a[1]*b[1],a[2]*b[0]+a[3]*b[1]};
        rep(i,0,2)ret[i].shrink();
        return ret;
    }
    template<typename T>Mat<T> operator*(const Mat<T>& a,const Mat<T>& b){
        Mat<T> ret={a[0]*b[0]+a[1]*b[2],a[0]*b[1]+a[1]*b[3],
            a[2]*b[0]+a[3]*b[2],a[2]*b[1]+a[3]*b[3]};
        rep(i,0,4)ret[i].shrink();
        return ret;
    }
    
    template<typename T>Mat<T> HGCD(P<T> a){
        int m=(SZ(a[0])+1)>>1;
        if(SZ(a[1])<=m){
            Mat<T> ret;
            ret[0]={1},ret[3]={1};
            return ret;
        }
        auto R=HGCD(P<T>{a[0]>>m,a[1]>>m});
        a=R*a;
        if(SZ(a[1])<=m)return R;
        Mat<T> Q;
        Q[1]={1},Q[2]={1},Q[3]=-(a[0]/a[1]);
        R=Q*R,a=Q*a;
        if(SZ(a[1])<=m)return R;
        int k=2*m+1-SZ(a[0]);
        auto H=HGCD(P<T>{a[0]>>k,a[1]>>k});
        return H*R;
    }
    template<typename T>Mat<T> InnerGCD(P<T> a){
        if(SZ(a[0])<SZ(a[1])){
            auto M=InnerGCD(P<T>{a[1],a[0]});
            swap(M[0],M[1]);
            swap(M[2],M[3]);
            return M;
        }
        auto m0=HGCD(a);
        a=m0*a;
        if(a[1].empty())return m0;
        Mat<T> Q;
        Q[1]={1},Q[2]={1},Q[3]=-(a[0]/a[1]);
        m0=Q*m0,a=Q*a;
        if(a[1].empty())return m0;
        return InnerGCD(a)*m0;
    }
    template<typename T>T gcd(const T& a,const T& b){
        P<T> p({a,b});
        auto M=InnerGCD(p);
        p=M*p;
        if(!p[0].empty()){
            auto coeff=p[0].back().inv();
            for(auto& x:p[0])x*=coeff;
        }
        return p[0];
    }
    template<typename T>pair<bool,T> PolyInv(const T& a,const T& b){
        P<T> p({a,b});
        auto M=InnerGCD(p);
        T g=(M*p)[0];
        if(g.size()!=1)return {false,{}};
        P<T> x({T({1}),b});
        auto ret=(M*x)[0]%b;
        auto coeff=g[0].inv();
        for(auto& x:ret)x*=coeff;
        return {true,ret};
    }
}

/**
 * @brief Half GCD
*/
#line 13 "sol.cpp"

FastIO io;
int main(){
    int M,K,R;
    io.read(M,K,R);

    Poly<Fp> h(K+1);
    const Fp invm=Fp(M).inv();
    const Fp invkm=Fp(ll(K)*M).inv();
    rep(i,1,K+1)h[i]=invkm;
    h[0]=-invm;    

    Poly<Fp> pw({0,1}),one({1}),rem,base({1});
    while(M){
        if(M&1){
            rem+=one*base;
            base*=pw;
            rem%=h;
            base%=h;
        }
        M>>=1;
        one+=one*pw;
        one%=h;
        pw*=pw;
        pw%=h;
    }

    auto [_,P]=HalfGCD::PolyInv(rem,h);
    P+=Poly<Fp>({-1,1});
    h*=Poly<Fp>({-1,1});
    Fp ret=nth(P,h,R)-nth(P,h,0);
    io.write(ret.v);
    return 0;
}