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 |
 tko919
|
| 提出日時 | 2020-04-29 02:26:54 |
| 言語 | C++14 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 8,243 bytes |
| コンパイル時間 | 3,055 ms |
| コンパイル使用メモリ | 210,252 KB |
| 実行使用メモリ | 76,156 KB |
| 最終ジャッジ日時 | 2023-08-17 14:03:42 |
| 合計ジャッジ時間 | 9,039 ms |
|
ジャッジサーバーID （参考情報） |
judge14 / judge12 |
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<class T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<class T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end
template<typename T=int>inline T get(){
char c=getchar(); bool neg=(c=='-');
T res=neg?0:c-'0'; while(isdigit(c=getchar()))res=res*10+(c-'0');
return neg?-res:res;
}
template<typename T=int>inline void put(T x,char c='\n'){
if(x<0)putchar('-'),x*=-1; int d[20],i=0;
do{d[i++]=x%10;}while(x/=10); while(i--)putchar('0'+d[i]);
putchar(c);
}
template<unsigned mod=1000000007>struct fp {
unsigned v;
static unsigned get_mod(){return mod;}
unsigned 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():v(0){}
fp(ll x):v(x>=0?x%mod:mod+(x%mod)){}
fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;}
fp& operator+=(const fp& x){if((v+=x.v)>=mod)v-=mod;return *this;}
fp& operator-=(const fp& x){if((v+=mod-x.v)>=mod)v-=mod; return *this;}
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;}
}; using Fp=fp<>;
template<typename T>struct factorial {
vector<T> Fact,Finv,Inv;
factorial(int maxx){
Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);
Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1; unsigned mod=Fp::get_mod();
rep(i,2,maxx){
Fact[i]=Fact[i-1]*i;
Inv[i]=Inv[mod%i]*(mod-mod/i);
Finv[i]=Finv[i-1]*Inv[i];
}
}
T fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];}
T inv(int n){return Inv[n];}
T nPr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[n-r];}
T nCr(int n,int r){if(n<0||n<r||r<0)return Fp(0);else return Fact[n]*Finv[r]*Finv[n-r];}
};
template<typename T,unsigned p>struct NTT{
vector<T> rt,irt;
NTT(int lg=21){
const unsigned m=T(-1).v; T prt=p;
rt.resize(1<<lg,1); irt.resize(1<<lg,1);
for(int w=0;w<lg;w++){
int mask=1<<w; T g=prt.pow(m>>w),ig=g.inv();
for(int i=0;i<mask-1;i++){
rt[mask+i+1]=g*rt[mask+i];
irt[mask+i+1]=ig*irt[mask+i];
}
}
}
void ntt(vector<T>& f,bool inv=0){
int n=f.size();
if(inv){
for(int i=1;i<n;i<<=1)for(int j=0;j<n;j+=i*2)for(int k=0;k<i;k++){
f[i+j+k]*=irt[i*2+k]; const T tmp=f[j+k]-f[i+j+k];
f[j+k]+=f[i+j+k]; f[i+j+k]=tmp;
} T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;
}else{
for(int i=n>>1;i;i>>=1)for(int j=0;j<n;j+=i*2)for(int k=0;k<i;k++){
const T tmp=f[j+k]-f[i+j+k];
f[j+k]+=f[i+j+k]; f[i+j+k]=tmp*rt[i*2+k];
}
}
}
vector<T> conv(vector<T> a,vector<T> b,bool same){
int n=a.size()+b.size()-1,m=1; while(m<n)m<<=1;
a.resize(m); ntt(a);
if(same)rep(i,0,m)a[i]*=a[i];
else{b.resize(m); ntt(b); rep(i,0,m)a[i]*=b[i];}
ntt(a,1); a.resize(n); return a;
}
};
using M1=fp<1045430273>; using M2=fp<1051721729>; using M3=fp<1053818881>;
NTT<fp<1045430273>,3> N1; NTT<fp<1051721729>,6> N2; NTT<fp<1053818881>,7> N3;
inline vector<Fp> multiply(vector<Fp> a,vector<Fp> b,bool same=0){
int n=a.size()+b.size()-1; vector<Fp> res(n); vector<int> vals[3];
vector<int> aa(a.size()),bb(b.size());
rep(i,0,a.size())aa[i]=a[i].v; rep(i,0,b.size())bb[i]=b[i].v;
vector<M1> a1(ALL(aa)),b1(ALL(bb)),c1=N1.conv(a1,b1,same);
vector<M2> a2(ALL(aa)),b2(ALL(bb)),c2=N2.conv(a2,b2,same);
vector<M3> a3(ALL(aa)),b3(ALL(bb)),c3=N3.conv(a3,b3,same);
for(M1 x:c1)vals[0].push_back(x.v);
for(M2 x:c2)vals[1].push_back(x.v);
for(M3 x:c3)vals[2].push_back(x.v);
M2 r_12=175287122;
M3 r_13=395182206,r_23=526909943,r_1323=461108887;
Fp w1=1045430273; Fp w2=571989935;
rep(i,0,n){
ll a=vals[0][i];
ll b=(vals[1][i]+M2::get_mod()-a)*r_12.v%M2::get_mod();
ll c=((vals[2][i]+M3::get_mod()-a)*r_1323.v+
(M3::get_mod()-b)*r_23.v)%M3::get_mod();
res[i]=(a+b*w1.v+c*w2.v);
} return res;
}
factorial<Fp> fact(1048576); inline Fp Inv(int x){return fact.inv(x);}
template<typename T>struct Poly{
vector<T> f;
Poly(){}
Poly(int _n):f(_n){}
Poly(vector<T> _f){f=_f;}
T& operator[](const int i){return f[i];}
T eval(T x){T res,w=1; for(T v:f)res+=w*v,w*=x; return res;}
int size()const{return f.size();}
Poly resize(int n){Poly res=*this; res.f.resize(n); return res;}
void shrink(){while(!f.empty() and f.back()==0)f.pop_back();}
Poly inv()const{
assert(f[0]!=0); int n=f.size(); Poly res(1); res[0]=f[0].inv();
for(int k=1;k<n;k<<=1){
Poly g=res,h=*this; h=h.resize(k*2); res=res.resize(k*2);
g=(g.square()*h).resize(k*2); rep(i,k,min(k*2,n))res[i]-=g[i];
} return res;
}
Poly square(){return Poly(multiply(f,f,1));}
Poly operator+(const Poly& g)const{return Poly(*this)+=g;}
Poly operator-(const Poly& g)const{return Poly(*this)-=g;}
Poly operator*(const Poly& g)const{return Poly(*this)*=g;}
Poly operator/(const Poly& g)const{return Poly(*this)/=g;}
Poly operator%(const Poly& g)const{return Poly(*this)%=g;}
Poly& operator+=(Poly g){
if(g.size()>f.size())f.resize(g.size());
rep(i,0,g.size())f[i]+=g[i]; shrink(); return *this;
}
Poly& operator-=(Poly g){
if(g.size()>f.size())f.resize(g.size());
rep(i,0,g.size())f[i]-=g[i]; shrink(); return *this;
}
Poly& operator*=(Poly g){f=multiply(f,g.f); shrink(); return *this;}
Poly& operator/=(Poly g){
if(g.size()>f.size())return *this=Poly();
reverse(ALL(f)); reverse(ALL(g.f));
int n=f.size()-g.size()+1;
f.resize(n); g.f.resize(n);
*this*=g.inv(); f.resize(n);
reverse(ALL(f)); shrink(); return *this;
}
Poly& operator%=(Poly g){*this-=*this/g*g; shrink(); return *this;}
Poly diff(){Poly res(f.size()-1); rep(i,0,res.size())res[i]=f[i+1]*(i+1); return res;}
Poly inte(){Poly res(f.size()+1); for(int i=res.size()-1;i;i--)res[i]=f[i-1]*Inv(i); return res;}
Poly log(){
assert(f[0]==1); int n=f.size(); Poly res=diff()*inv();
res=res.inte(); return res.resize(n);
}
Poly exp(){
assert(f[0]==0); int n=f.size();
Poly res(1),g(1); res[0]=g[0]=1;
for(int k=1;k<n;k<<=1){
g=(g+g-g.square()*res).resize(k);
Poly q=resize(k).diff();
Poly w=(q+g*(res.diff()-res*q)).resize(2*k-1);
res=(res+res*(resize(k*2)-w.inte())).resize(2*k);
} return res.resize(n);
}
Poly shift(int c){
int n=f.size(); Poly res=*this,mul(n);
factorial<T> fact(n+1); mul[1]=c; mul=mul.exp();
rep(i,0,n)res[i]*=fact.fact(i); reverse(ALL(res.f));
res*=mul; res=res.resize(n); reverse(ALL(res.f));
rep(i,0,n)res[i]*=fact.fact(i,1); return res;
}
};
int a[]={2,3,5,7,11,13},b[]={4,6,8,9,10,12};
ll n; int m; Fp dp[2][310][4000]; Poly<Fp> g;
Fp ktms(ll t){
Poly<Fp> ret({Fp(1)}),mul({Fp(0),Fp(1)});
while(t){
if(t&1)ret=ret*mul,ret%=g;
mul=(mul*mul)%g; t>>=1;
} Fp res; for(auto x:ret.f)res+=x; return res;
}
int main(){
int p,c; cin>>n>>p>>c;
m=p*13+c*12; dp[0][0][0]=dp[1][0][0]=1;
rep(k,0,6)rep(i,0,p)rep(j,0,p*13-a[k]+1)if(dp[0][i][j]!=0)dp[0][i+1][j+a[k]]+=dp[0][i][j];
rep(k,0,6)rep(i,0,c)rep(j,0,c*12-b[k]+1)if(dp[1][i][j]!=0)dp[1][i+1][j+b[k]]+=dp[1][i][j];
m++; g.f.resize(m); rep(i,0,p*13+1)rep(j,0,c*12+1)g[i+j]+=dp[0][p][i]*dp[1][c][j];
reverse(ALL(g.f)); for(auto& x:g.f)x*=-1; g.f.back()=1;
Fp res=ktms(n+m-2); printf("%d\n",res.v);
return 0;
}