結果

問題 No.215 素数サイコロと合成数サイコロ (3-Hard)
ユーザー maroon_kurimaroon_kuri
提出日時 2019-05-23 14:45:11
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,823 ms / 4,000 ms
コード長 11,795 bytes
コンパイル時間 2,514 ms
コンパイル使用メモリ 195,976 KB
実行使用メモリ 41,340 KB
最終ジャッジ日時 2024-09-17 09:45:54
合計ジャッジ時間 7,809 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1,724 ms
40,848 KB
testcase_01 AC 1,823 ms
41,340 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) FOR(i,0,b)
#define ROF(i,a,b) for(int i=int(b)-1;i>=a;i--)
#define per(i,b) ROF(i,0,b)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define reach cerr<<"reached"<<endl
void dmpr(decltype(cerr)&os){os<<endl;}
template<class T,class... Args>
void dmpr(decltype(cerr)&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp(...) dmpr(cerr,##__VA_ARGS__)
#define zero(x) memset(x,0,sizeof(x))
#define one(x) memset(x,-1,sizeof(x))
#define fs first
#define sc second
#define bg begin()
#define ed end()

template<class T> using V=vector<T>;
template<class T> using VV=V<V<T>>;

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	rep(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

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<<")";
}

ll read(){
	ll i;
	scanf("%lld",&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%lld",x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

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(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

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>
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);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

constexpr ll TEN(int n){
	return n==0?1:TEN(n-1)*10;
}

template<class T>
vector<T> uni(const vector<T>&vv){
	auto v(vv);
	sort(all(v));
	v.erase(unique(all(v)),v.end());
	return v;
}
template<class T>
void mkuni(vector<T>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.end());
}

//ayasii
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 popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

#define SMOD

#ifdef SMOD
template<uint mod>
#else
uint mod;
#endif
struct ModInt{
	#ifdef SMOD
	static constexpr uint base=mod;
	#else
	static constexpr uint& base=mod;
	#endif
	uint v;
	ModInt():v(0){}
	ModInt(ll vv){
		s(vv%mod+mod);
	}
	ModInt& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	explicit operator bool()const{
		return v;
	}
	explicit operator int()const{
		return v;
	}
	bool operator==(const ModInt&rhs)const{
		return v==rhs.v;
	}
	bool operator!=(const ModInt&rhs)const{
		return v!=rhs.v;
	}
	ModInt operator-()const{
		return ModInt()-*this;
	}
	ModInt& operator+=(const ModInt&rhs){
		return s(v+rhs.v);
	}
	ModInt&operator-=(const ModInt&rhs){
		return s(v+mod-rhs.v);
	}
	ModInt&operator*=(const ModInt&rhs){
		v=ull(v)*rhs.v%mod;
		return *this;
	}
	ModInt&operator/=(const ModInt&rhs){
		return *this*=rhs.inv();
	}
	ModInt operator+(const ModInt&rhs)const{
		return ModInt(*this)+=rhs;
	}
	ModInt operator-(const ModInt&rhs)const{
		return ModInt(*this)-=rhs;
	}
	ModInt operator*(const ModInt&rhs)const{
		return ModInt(*this)*=rhs;
	}
	ModInt operator/(const ModInt&rhs)const{
		return ModInt(*this)/=rhs;
	}
	friend ModInt operator+(int x,const ModInt&y){
		return ModInt(x)+y;
	}
	friend ModInt operator-(int x,const ModInt&y){
		return ModInt(x)-y;
	}
	friend ModInt operator*(int x,const ModInt&y){
		return ModInt(x)*y;
	}
	friend ModInt operator/(int x,const ModInt&y){
		return ModInt(x)/y;
	}
	ModInt pow(int n)const{
		ModInt res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	ModInt inv()const{
		return pow(mod-2);
	}
};

#ifdef SMOD
template<uint mod>
ostream& operator<<(ostream&os,const ModInt<mod>&m){
	return os<<m.v;
}
template<uint mod>
void print(const ModInt<mod>&m,int suc=1){
	print(m.v,suc);
}
#else
ostream& operator<<(ostream&os,const ModInt&m){
	return os<<m.v;
}
void print(const ModInt&m,int suc=1){
	print(m.v,suc);
}
#endif

#ifdef SMOD
using mint=ModInt<1000000007>;
//using mint=ModInt<998244353>;
#else
using mint=ModInt;
#endif

const int Vmax=2000010;
mint fact[Vmax],factInv[Vmax],invs[Vmax];
void InitFact(){
	fact[0]=1;
	FOR(i,1,Vmax){
		fact[i]=fact[i-1]*i;
	}
	factInv[Vmax-1]=fact[Vmax-1].inv();
	for(int i=Vmax-2;i>=0;i--){
		factInv[i]=factInv[i+1]*(i+1);
	}
	for(int i=Vmax-1;i>=1;i--){
		invs[i]=factInv[i]*fact[i-1];
	}
}
#ifdef SMOD
struct InitFactDummy{
	InitFactDummy(){
		InitFact();
	}
} initFactDummy;
#endif
mint Choose(int n,int k){
	return fact[n]*factInv[n-k]*factInv[k];
}
mint Binom(int a,int b){
	return fact[a+b]*factInv[a]*factInv[b];
}
mint Catalan(int n){
	return Binom(n,n)-(n-1>=0?Binom(n-1,n+1):0);
}

static const int S=1<<18;
using R=double;

using C=complex<R>;

C& operator*=(C &a,C b){
	return a=C(a.real()*b.real()-a.imag()*b.imag(),a.real()*b.imag()+a.imag()*b.real());
}
C operator*(const C&a,C b){
	return C(a.real()*b.real()-a.imag()*b.imag(),a.real()*b.imag()+a.imag()*b.real());
}

void inplace_fft(V<C>&f,bool inv){
	static const R P=acos(-1);
	static C r[S],ir[S];
	static bool did=false;
	if(!did){
		rep(i,S){
			R a=2*P/S*i;
			r[i]=C(cos(a),sin(a));
			ir[i]=conj(r[i]);
		}
		did=true;
	}
	const int n=f.size();
	V<C> g(n);
	for(int b=n/2;b>=1;b/=2){
		int w=S/(n/b),p=0;
		for(int i=0;i<n;i+=b*2){
			rep(j,b){
				f[i+j+b]*=inv?ir[p]:r[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]/=n;
}
/*
//for doubles
V<C> convolution(V<C> x,V<C> y){
	int n=x.size()+y.size()-1;
	int s=1;
	while(s<n)s*=2;
	x.resize(s);inplace_fft(x,false);
	y.resize(s);inplace_fft(y,false);
	rep(i,s)
		x[i]*=y[i];
	inplace_fft(x,true);x.resize(n);
	return x;
}

template<class D>
V<D> multiply(const V<D>&x,const V<D>&y){
	const auto ch=[&](const V<D>& v){
		V<C> r(v.size());
		rep(i,v.size())
			r[i]=v[i];
		return r;
	};
	auto z=convolution(ch(x),ch(y));
	V<D> r(z.size());
	rep(i,z.size())
		r[i]=z[i].real();
	return r;
}

R invs[S];
struct InitRInvs{
	InitRInvs(){
		FOR(i,1,S)
			invs[i]=1/i;
	}
} InitRInvsDummy;*/

V<mint> multiply(const V<mint>&x,const V<mint>&y){
	const int B=15;
	int n=x.size()+y.size()-1;
	if(x.size()<8||y.size()<8){
		V<mint> r(n);
		rep(i,x.size())rep(j,y.size())
			r[i+j]+=x[i]*y[j];
		return r;
	}
	int s=1;
	while(s<n)s*=2;
	const auto ch=[&](const V<mint>&v){
		V<C> r(s);
		rep(i,v.size())
			r[i]=C(v[i].v&((1<<B)-1),v[i].v>>B);
		return r;
	};
	V<C> a=ch(x),b=ch(y);
	inplace_fft(a,false);
	inplace_fft(b,false);
	V<C> c(s),d(s);
	rep(i,s){
		int j=(s-i)%s;
		C xl=(a[i]+conj(a[j]))*C(0.5,0);
		C xh=(a[i]-conj(a[j]))*C(0,-0.5);
		c[i]=xl*b[i];
		d[i]=xh*b[i];
	}
	inplace_fft(c,true);
	inplace_fft(d,true);
	V<mint> r(n);
	rep(i,n){
		r[i]=mint(round(c[i].real()))
			+mint(round(c[i].imag()))*(1<<B)
			+mint(round(d[i].real()))*(1<<B)
			+mint(round(d[i].imag()))*(1<<B*2);
	}
	return r;
}

template<class D>
struct Poly:public V<D>{
	template<class...Args>
	Poly(Args...args):V<D>(args...){}
	Poly(initializer_list<D>init):V<D>(all(init)){}
	int size()const{
		return V<D>::size();
	}
	void ups(int s){
		if(size()<s)this->resize(s,0);
	}
	Poly low(int s)const{
		return Poly(this->bg,this->bg+min(s,size()));
	}
	Poly rev()const{
		auto r=*this;
		reverse(all(r));
		return r;
	}
	Poly& operator+=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]+=r[i];
		return *this;
	}
	Poly& operator-=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]-=r[i];
		return *this;
	}
	template<class T>
	Poly& operator*=(T t){
		for(auto&v:*this)
			v*=t;
		return *this;
	}
	Poly& operator*=(const Poly&r){
		return *this=multiply(*this,r);
	}
	Poly inv(int s)const{
		Poly r{1/(*this)[0]};
		for(int n=1;n<s;n*=2)
			r=r*2-(r*r*low(2*n)).low(2*n);
		return r.low(s);
	}
	template<class T>
	Poly& operator/=(T t){
		return *this*=1/D(t);
	}
	Poly& operator/=(const Poly&r){
		int m=r.size();
		assert(r[m-1]);
		int n=size();
		int s=n-m+1;
		if(s<=0) return *this={};
		return *this=(rev().low(s)*r.rev().inv(s)).low(s).rev();
	}
	Poly& operator%=(const Poly&r){
		*this-=*this/r*r;
		return *this=low(r.size()-1);
	}
	Poly operator+(const Poly&r)const{return Poly(*this)+=r;}
	Poly operator-(const Poly&r)const{return Poly(*this)-=r;}
	template<class T>
	Poly operator*(T t)const{return Poly(*this)*=t;}
	Poly operator*(const Poly&r)const{return Poly(*this)*=r;}
	template<class T>
	Poly operator/(T t)const{return Poly(*this)/=t;}
	Poly operator/(const Poly&r)const{return Poly(*this)/=r;}
	Poly operator%(const Poly&r)const{return Poly(*this)%=r;}
	Poly dif()const{
		Poly r(max(int(0),size()-1));
		rep(i,r.size())
			r[i]=(*this)[i+1]*(i+1);
		return r;
	}
	Poly inte()const{
		Poly r(size()+1,0);
		rep(i,size())
			r[i+1]=(*this)[i]*invs[i+1];
		return r;
	}
	//opencupXVIII GP of Peterhof H
	Poly log(int s)const{
		return (low(s).dif()*inv(s-1)).low(s-1).inte();
	}
	//Petrozavodsk 2019w Day1 G
	Poly exp(int s)const{
		return exp2(s).fs;
	}
	pair<Poly,Poly> exp2(int s)const{
		assert((*this)[0]==0);
		Poly f{1},g{1};
		for(int n=1;;n*=2){
			if(n>=s)break;
			g=g*2-(g*g*f).low(n);
			//if(n>=s)break;
			Poly q=low(n).dif();
			q=q+g*(f.dif()-f*q).low(2*n-1);
			f=f+(f*(low(2*n)-q.inte())).low(2*n);
		}
		return mp(f.low(s),g.low(s));
	}
	//CF250 E
	Poly sqrt(int s)const{
		assert((*this)[0]==1);
		Poly r{1};
		for(int n=1;n<s;n*=2)
			r=(r+(r.inv(n*2)*low(n*2)).low(n*2))*invs[2];
		return r.low(s);
	}
};

using P=Poly<mint>;
P gen(vi vs,int c){
	int n=vs.back()*c;
	VV<mint> dp(n+1,V<mint>(c+1));
	dp[0][0]=1;
	for(auto v:vs)
		rep(i,n-v+1)rep(j,c)
			dp[i+v][j+1]+=dp[i][j];
	P res(n+1);
	rep(i,n+1)
		res[i]=dp[i][c];
	return res;
}

signed main(){
	int n=read(),p=read(),c=read();
	auto w=gen({2,3,5,7,11,13},p)*gen({4,6,8,9,10,12},c);
	int s=n+w.size()-2;
	cerr<<s<<endl;
	w[0]=-1;
	w=w.rev();
	cerr<<w<<endl;
	P cur{1},x{0,1};
	while(s){
		if(s%2)
			cur=cur*x%w;
		x=x*x%w;
		s/=2;
	}
	dmp(cur);
	print(accumulate(all(cur),mint(0)));
}
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