#593096 (C++17) No.802 だいたい等差数列

• 問題: No.802 だいたい等差数列
• ユーザー: mugen_1337
• 提出日時: 2020-12-14 10:46:32
• 言語: C++17 (gcc 13.3.0 + boost 1.89.0)
• 結果: TLE
• 実行時間: -
• コード長: 9,263 bytes
• コンパイル時間: 3,329 ms
• コンパイル使用メモリ: 208,208 KB
• 最終ジャッジ日時: 2025-01-17 00:28:32
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
sample	AC * 3 TLE * 1
other	AC * 1 WA * 1 TLE * 28

ソースコード

#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;
}
 
template<ll Mod>
struct ModInt{
    long long x;
    ModInt():x(0){}
    ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%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;}
};
using mint=ModInt<mod>;
 
template<typename T>
struct FormalPowerSeries:vector<T>{
    using vector<T>::vector;
    using P=FormalPowerSeries;
    using MULT=function<P(P,P)>;
 
    static MULT &get_mult(){static MULT mult=nullptr;return mult;}
    static void set_mult(MULT f){get_mult()=f;}
    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);
        }
        assert(get_mult()!=nullptr);
        return (*this)=get_mult()(*this,rhs);
    }
    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;
    }
    // 微分
    P diff()const{
        const int n=(int)this->size();
        P ret(max(0,n-1));
        for(int i=1;i<n;i++) ret[i-1]=(*this)[i]*T(i);
        return ret;
    }
    // 積分
    P integral()const{
        const int n=(int)this->size();
        P ret(n+1);
        ret[0]=T(0);
        for(int i=0;i<n;i++) ret[i+1]=(*this)[i]/T(i+1);
        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);
    }
    // ?
    P log(int deg=-1)const{
        assert((*this)[0]==1);
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        return (this->diff()*this->inv(deg)).pre(deg-1).integral();
    }
    // ?
    P exp(int deg=-1)const{
        assert((*this)[0]==T(0));
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        P ret({T(1)});
        for(int i=1;i<deg;i<<=1) ret=(ret*(pre(i<<1)+T(1)-ret.log(i<<1))).pre(i<<1);
        return ret.pre(deg);
    }
    // O(nlogn) with NTT
    // 
    P pow_fast(long long k,int deg=-1){
        int n=(int)this->size();
        if(deg==-1) deg=n;
        for(int i=0;i<n;i++){
            if((*this)[i]!=T(0)){
                T rev=T(1)/(*this)[i];
                P ret=(((*this*rev)>>i).log()*k).exp()*((*this)[i].pow(k));
                if(i*k>deg) return P(deg,T(0));
                ret=(ret<<(i*k)).pre(deg);
                if((int)ret.size()<deg) ret.resize(deg,T(0));
                return ret;
            }
        }
        return *this;
    }
    // O(Mult * log k)
    // resize not verified
    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),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);
    }
};
using FPS=FormalPowerSeries<mint>;
 
auto multiply_naive(const FPS::P &lhs,const FPS::P &rhs){
    assert(!lhs.empty() and !rhs.empty());
    auto ret=FPS(int(lhs.size())+int(rhs.size())-1);
    rep(i,(int)lhs.size())rep(j,(int)rhs.size()) ret[i+j]+=lhs[i]*rhs[j];
    return ret;
}

/*

B = x^0 + x^1 + ... + x^m-1
P = ((x^d1 - x^d2) / (1 - x)) ^ (n-1)

B*Pの0~m-1項の和が答え

1e9+7で間に合うのかとかの感覚がないし
FPSのライブラリへの理解とかが少ないので解けるのかもわからない
ここからDPかなんかへのアプローチの転換をしたい．
また今度
*/

signed main(){
    FPS::set_mult(multiply_naive);

    int n,m,d1,d2;cin>>n>>m>>d1>>d2;

    FPS B(m,1);
    FPS P(m);
    if(d1<d2){
        P[d1]=1;
        if(d2+1<m) P[d2+1]=-1;
        P/=FPS{1,-1};
    }else{
        if(d1<m) P[d1]=1;
    }

    rep(i,n-1){
        B*=P;
        B.resize(m);
    }

    // debug(B);
    mint res=0;
    rep(i,m) res+=B[i];
    cout<<res<<endl;
    return 0;
}