test/yuki473.test.cpp

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• Last update: 2023-07-16 21:56:51+09:00
• Problem: https://yukicoder.me/problems/473

Depends on

• Math/FormalPowerSeriesNaive.hpp
• template.hpp
• type/modint.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/473"

#include "../template.hpp"

#include "../type/modint.hpp"

using mint=ModInt<1000000007>;

#include "../Math/FormalPowerSeriesNaive.hpp"

using FPS=FormalPowerSeriesNaive<mint>;

signed main(){
    int n,s,k;cin>>n>>s>>k;
    s-=n*(n-1)/2*k;
    if(s<0){
        cout<<0<<endl;
        return 0;
    }

    FPS den{1},num{1};
    for(int i=1;i<=n;i++) den-=(den<<i);
    cout<<num.nth_term(den,s)<<endl;
    return 0;
}

#line 1 "test/yuki473.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/473"

#line 1 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

#line 4 "test/yuki473.test.cpp"

#line 1 "type/modint.hpp"
template<int Mod>
struct ModInt{
    int x;
    ModInt():x(0){}
    ModInt(int y): x (y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod){}
    ModInt(long long y){
        if (y >= 0)
        {
            x = (int)(y % (ll)(Mod));
        }
        else
        {
            int tmp = (int)((-y) % (ll)Mod);
            x = (Mod - tmp) % Mod;
        }
    }
    ModInt &operator+=(const ModInt &p){
        if((x += p.x) >= Mod) x -= Mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p){
        if((x += Mod - p.x) >= Mod) x -= Mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p){
        x = (int)(1ll * x * p.x % Mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p){
        (*this) *= p.inverse();
        return *this;
    }
    ModInt operator-()const{return ModInt(-x);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    bool operator==(const ModInt &p)const{return x==p.x;}
    bool operator!=(const ModInt &p)const{return x!=p.x;}
    ModInt inverse()const{
        int a = x, b = Mod ,u = 1, v = 0, t;
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);swap(u-=t*v,v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n)const{
        ModInt ret(1),mul(x);
        while(n>0){
            if(n&1) ret*=mul;
            mul*=mul;n>>=1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
    friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
    static int get_mod(){return Mod;}
};
#line 6 "test/yuki473.test.cpp"

using mint=ModInt<1000000007>;

#line 1 "Math/FormalPowerSeriesNaive.hpp"
template<typename T>
struct FormalPowerSeriesNaive:vector<T>{
    using vector<T>::vector;
    using P=FormalPowerSeriesNaive;

    P multiply(const P &lhs,const P &rhs){
        auto ret=P((int)lhs.size()+rhs.size()-1);
        for(int i=0;i<(int)lhs.size();i++)for(int j=0;j<(int)rhs.size();j++) ret[i+j]+=lhs[i]*rhs[j];
        return ret;
    }

    void shrink(){while(this->size() and this->back()==T(0)) this->pop_back();}
    P pre(int sz)const{return P(begin(*this),begin(*this)+min((int)this->size(),sz));}
    P operator+(const P &rhs)const{return P(*this)+=rhs;}
    P operator+(const T &rhs)const{return P(*this)+=rhs;}
    P operator-(const P &rhs)const{return P(*this)-=rhs;}
    P operator-(const T &rhs)const{return P(*this)-=rhs;}
    P operator*(const P &rhs)const{return P(*this)*=rhs;}
    P operator*(const T &rhs)const{return P(*this)*=rhs;}
    P operator/(const P &rhs)const{return P(*this)/=rhs;}
    P operator%(const P &rhs)const{return P(*this)%=rhs;}
    P &operator+=(const P &rhs){
        if(rhs.size()>this->size()) this->resize(rhs.size());
        for(int i=0;i<(int)rhs.size();i++) (*this)[i]+=rhs[i];
        return (*this);
    }
    P &operator+=(const T &rhs){
        if(this->empty()) this->resize(1);
        (*this)[0]+=rhs;
        return (*this);
    }
    P &operator-=(const P &rhs){
        if(rhs.size()>this->size()) this->resize(rhs.size());
        for(int i=0;i<(int)rhs.size();i++) (*this)[i]-=rhs[i];
        shrink();
        return (*this);
    }
    P &operator-=(const T &rhs){
        if(this->empty()) this->resize(1);
        (*this)[0]-=rhs;
        shrink();
        return (*this);
    }
    P &operator*=(const T &rhs){
        const int n=(int)this->size();
        for(int i=0;i<n;i++) (*this)[i]*=rhs;
        return (*this);
    }
    P &operator*=(const P &rhs){
        if(this->empty() or rhs.empty()){
            this->clear();
            return (*this);
        }
        auto ret=multiply(*this,rhs);
        (*this)=ret;
        return (*this);
    }
    P &operator%=(const P &rhs){return (*this)-=(*this)/rhs*rhs;}
    P operator-()const{
        P ret(this->size());
        for(int i=0;i<(int)this->size();i++) ret[i]=-(*this)[i];
        return ret;
    }
    P &operator/=(const P &rhs){
        if(this->size()<rhs.size()){
            this->clear();
            return (*this);
        }
        int n=(int)this->size()-rhs.size()+1;
        return (*this)=(rev().pre(n)*rhs.rev().inv(n));
    }
    P operator>>(int sz)const{
        if((int)this->size()<=sz) return {};
        P ret(*this);
        ret.erase(ret.begin(),ret.begin()+sz);
        return ret;
    }
    P operator<<(int sz)const{
        P ret(*this);
        ret.insert(ret.begin(),sz,T(0));
        return ret;
    }
    P rev(int deg=-1)const{
        P ret(*this);
        if(deg!=-1) ret.resize(deg,T(0));
        reverse(begin(ret),end(ret));
        return ret;
    }
    // ref : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
    P inv(int deg=-1)const{
        assert(((*this)[0])!=T(0));
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        P ret({T(1)/(*this)[0]});
        for(int i=1;i<deg;i<<=1) ret=(ret+ret-ret*ret*pre(i<<1)).pre(i<<1);
        return ret.pre(deg);
    }
    // O(Mult * log k)
    P pow(ll k,int deg=-1){
        if(deg==-1) deg=1000000000;
        P ret=P{1};
        P b(*this);
        while(k){
            if(k&1) ret*=b;
            b=b*b;
            k>>=1;
            if((int)ret.size()>deg) ret.resize(deg);
            if((int)b.size()>deg) b.resize(deg);
        }
        return ret;
    }
    // [l,r) k個飛び
    P slice(int l,int r,int k=1){
        P ret;
        for(int i=l;i<r;i+=k) ret.push_back((*this)[i]);
        return ret;
    }
    /*
    ref : https://atcoder.jp/contests/aising2020/submissions/15300636
          http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
 
    order :      
        O(M(d)log(k))  (M(d) -> d次元，multiplyの計算量)
 
    return :
        [x^k] (*this) / q
    */
    T nth_term(P q,ll k){
        if(k==0) return (*this)[0]/q[0];
        P p(*this);
        P q_=q;
        for(int i=1;i<(int)q_.size();i+=2) q_[i]*=-1;
        q*=q_;p*=q_;// qは奇数項が消える
        return p.slice(k%2,p.size(),2).nth_term(q.slice(0,q.size(),2),k/2);
    }


    /*
    a_i = sum{j=1}^{d} c_j * a_{i-j}
    return c
    */
    P berlekamp_massey(){
        int N=(int)this->size();
        P b={T(-1)},c={T(-1)};
        T y=T(1);

        for(int ed=1;ed<=N;ed++){
            int l=(int)c.size(),m=(int)b.size();
            T x=0;
            for(int i=0;i<l;i++) x+=c[i]*(*this)[ed-l+i];
            b.emplace_back(0);
            m++;
            if(x==T(0)) continue;
            T freq=x/y;
            if(l<m){
                auto tmp=c;
                c.insert(begin(c),m-l,T(0));
                for(int i=0;i<m;i++) c[m-1-i]-=freq*b[m-1-i];
                b=tmp;
                y=x;
            }else{
                for(int i=0;i<m;i++) c[l-1-i]-=freq*b[m-1-i];
            }
        }
        reverse(begin(c),end(c));
        return c;
    }

    // this[0], this[1] ... 
    // linear recurrence
    // -> return Nth term
    // verified : https://atcoder.jp/contests/kupc2021/submissions/26974136
    T nth_linear_recurrence(long long N){
        auto q=berlekamp_massey();
        assert(not q.empty() and q[0]!=T(0));
        if(N<(int)this->size()) return (*this)[N];
        auto p=this->pre((int)q.size()-1)*q;
        p.resize((int)q.size()-1);
        return p.nth_term(q,N);
    }
};
#line 10 "test/yuki473.test.cpp"

using FPS=FormalPowerSeriesNaive<mint>;

signed main(){
    int n,s,k;cin>>n>>s>>k;
    s-=n*(n-1)/2*k;
    if(s<0){
        cout<<0<<endl;
        return 0;
    }

    FPS den{1},num{1};
    for(int i=1;i<=n;i++) den-=(den<<i);
    cout<<num.nth_term(den,s)<<endl;
    return 0;
}

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