結果
| 問題 |
No.8046 yukicoderの過去問
|
| コンテスト | |
| ユーザー |
 beet
|
| 提出日時 | 2019-06-29 11:17:34 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 11,366 bytes |
| コンパイル時間 | 3,357 ms |
| コンパイル使用メモリ | 231,264 KB |
| 最終ジャッジ日時 | 2025-01-07 05:40:02 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 4 TLE * 5 |
ソースコード
#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
//BEGIN CUT HERE
constexpr int bmds(int x){
const int v[] = {1012924417, 924844033, 998244353,
897581057, 645922817};
return v[x];
}
constexpr int brts(int x){
const int v[] = {5, 5, 3, 3, 3};
return v[x];
}
template<int X>
struct NTT{
static constexpr int md = bmds(X);
static constexpr int rt = brts(X);
inline int add(int a,int b){
a+=b;
if(a>=md) a-=md;
return a;
}
inline int mul(int a,int b){
return 1LL*a*b%md;
}
inline int pow(int a,int b){
int res=1;
while(b){
if(b&1) res=mul(res,a);
a=mul(a,a);
b>>=1;
}
return res;
}
inline int inv(int x){
return pow(x,md-2);
}
// assume md % 4 = 1
// if md % 4 == 3, then x = a^{(md+1)/4}
inline int sqrt(int a){
if(a==0) return 0;
if(pow(a,(md-1)/2)!=1) return -1;
int q=md-1,m=0;
while(~q&1) q>>=1,m++;
mt19937 mt;
int z=mt()%md;
while(pow(z,(md-1)/2)!=md-1) z=mt()%md;
int c=pow(z,q),t=pow(a,q),r=pow(a,(q+1)/2);
while(m>1){
if(pow(t,1<<(m-2))!=1)
r=mul(r,c),t=mul(t,mul(c,c));
c=mul(c,c);
m--;
}
return r;
}
vector<vector<int> > rts,rrts;
void ensure_base(int n){
if((int)rts.size()>=n) return;
rts.resize(n);rrts.resize(n);
for(int i=1;i<n;i<<=1){
if(!rts[i].empty()) continue;
int w=pow(rt,(md-1)/(i<<1));
int rw=inv(w);
rts[i].resize(i);rrts[i].resize(i);
rts[i][0]=1;rrts[i][0]=1;
for(int k=1;k<i;k++){
rts[i][k]=mul(rts[i][k-1],w);
rrts[i][k]=mul(rrts[i][k-1],rw);
}
}
}
void ntt(vector<int> &a,bool f,int n=-1){
if(n==-1) n=a.size();
assert((n&(n-1))==0);
for(int i=0,j=1;j+1<n;j++){
for(int k=n>>1;k>(i^=k);k>>=1);
if(i>j) swap(a[i],a[j]);
}
for(int i=1;i<n;i<<=1){
for(int j=0;j<n;j+=i*2){
for(int k=0;k<i;k++){
int z=mul(a[i+j+k],f?rrts[i][k]:rts[i][k]);
a[i+j+k]=add(a[j+k],md-z);
a[j+k]=add(a[j+k],z);
}
}
}
if(f){
int tmp=inv(n);
for(Int i=0;i<n;i++) a[i]=mul(a[i],tmp);
}
}
vector<int> add(vector<int> as,vector<int> bs){
int sz=max(as.size(),bs.size());
vector<int> cs(sz,0);
for(int i=0;i<(int)as.size();i++) cs[i]=add(cs[i],as[i]);
for(int i=0;i<(int)bs.size();i++) cs[i]=add(cs[i],bs[i]);
return cs;
}
vector<int> sub(vector<int> as,vector<int> bs){
int sz=max(as.size(),bs.size());
vector<int> cs(sz,0);
for(int i=0;i<(int)as.size();i++) cs[i]=add(cs[i],as[i]);
for(int i=0;i<(int)bs.size();i++) cs[i]=add(cs[i],md-bs[i]);
return cs;
}
vector<int> multiply(vector<int> as,vector<int> bs){
int need=as.size()+bs.size()-1;
int sz=1;
while(sz<need) sz<<=1;
ensure_base(sz);
vector<int> f(sz),g(sz);
for(int i=0;i<(int)as.size();i++) f[i]=as[i];
for(int i=0;i<(int)bs.size();i++) g[i]=bs[i];
ntt(f,0);ntt(g,0);
for(int i=0;i<sz;i++) f[i]=mul(f[i],g[i]);
ntt(f,1);
f.resize(need);
return f;
}
vector<int> divide(vector<int> as,vector<int> bs){
assert(bs!=vector<int>(bs.size(),0));
assert(as.size()>=bs.size());
int need=as.size()-bs.size()+1;
if(as==vector<int>(as.size(),0)) return {0};
reverse(as.begin(),as.end());
reverse(bs.begin(),bs.end());
while(bs.back()==0){
assert(as.back()==0);
as.pop_back();
bs.pop_back();
}
reverse(as.begin(),as.end());
reverse(bs.begin(),bs.end());
int sz=1;
vector<int> rs({inv(bs[0])});
while(sz<(int)as.size()){
sz<<=1;
rs=sub(add(rs,rs),multiply(multiply(rs,rs),bs));
rs.resize(sz);
}
while(as.back()==0) as.pop_back();
while(rs.back()==0) rs.pop_back();
auto cs=multiply(as,rs);
cs.resize(need,0);
return cs;
}
vector<int> sqrt(vector<int> as){
if(as==vector<int>(as.size(),0)) return {0};
int dg=0;
reverse(as.begin(),as.end());
while(as.back()==0){
dg++;
as.pop_back();
assert(as.back()==0);
as.pop_back();
}
reverse(as.begin(),as.end());
int sz=1,inv2=inv(2);
vector<int> ss({sqrt(as[0])});
while(sz<(int)as.size()){
sz<<=1;
vector<int> ts(as);
if((sz+sz/2)<(int)ts.size()) ts.resize(sz+sz/2);
ss=add(ss,divide(ts,ss));
ss.resize(sz);
for(int &x:ss) x=mul(x,inv2);
}
reverse(ss.begin(),ss.end());
for(int i=0;i<dg;i++) ss.emplace_back(0);
reverse(ss.begin(),ss.end());
return ss;
}
};
struct ArbitraryModConvolution{
using ll = long long;
static NTT<0> ntt0;
static NTT<1> ntt1;
static NTT<2> ntt2;
static constexpr int pow(int a,int b,int md){
int res=1;
a=a%md;
while(b){
if(b&1) res=(ll)res*a%md;
a=(ll)a*a%md;
b>>=1;
}
return res;
}
static constexpr int inv(int x,int md){
return pow(x,md-2,md);
}
inline void garner(vector< vector<int> > &cs,int MOD){
static constexpr int r01=inv(ntt0.md,ntt1.md);
static constexpr int r02=inv(ntt0.md,ntt2.md);
static constexpr int r12=inv(ntt1.md,ntt2.md);
int m01 =(ll)ntt0.md*ntt1.md%MOD;
size_t sz=cs[0].size();
for(size_t i=0;i<sz;i++){
cs[1][i]=(ll)(cs[1][i]-cs[0][i])*r01%ntt1.md;
if(cs[1][i]<0) cs[1][i]+=ntt1.md;
cs[2][i]=(ll)(cs[2][i]-cs[0][i])*r02%ntt2.md;
cs[2][i]=(ll)(cs[2][i]-cs[1][i])*r12%ntt2.md;
if(cs[2][i]<0) cs[2][i]+=ntt2.md;
cs[0][i]+=(ll)cs[1][i]*ntt0.md%MOD;
if(cs[0][i]>=MOD) cs[0][i]-=MOD;
cs[0][i]+=(ll)cs[2][i]*m01%MOD;
if(cs[0][i]>=MOD) cs[0][i]-=MOD;
}
}
inline int add(int a,int b,int MOD){
a+=b;
if(a>=MOD) a-=MOD;
return a;
}
vector<int> add(vector<int> as,vector<int> bs,int MOD){
int sz=max(as.size(),bs.size());
vector<int> cs(sz,0);
for(int i=0;i<(int)as.size();i++) cs[i]=add(cs[i],as[i],MOD);
for(int i=0;i<(int)bs.size();i++) cs[i]=add(cs[i],bs[i],MOD);
return cs;
}
vector<int> sub(vector<int> as,vector<int> bs,int MOD){
int sz=max(as.size(),bs.size());
vector<int> cs(sz,0);
for(int i=0;i<(int)as.size();i++) cs[i]=add(cs[i],as[i],MOD);
for(int i=0;i<(int)bs.size();i++) cs[i]=add(cs[i],MOD-bs[i],MOD);
return cs;
}
vector<int> multiply(vector<int> as,vector<int> bs,int MOD){
for(int& x:as) x%=MOD;
for(int& x:bs) x%=MOD;
vector< vector<int> > cs(3);
cs[0]=ntt0.multiply(as,bs);
cs[1]=ntt1.multiply(as,bs);
cs[2]=ntt2.multiply(as,bs);
size_t sz=as.size()+bs.size()-1;
for(auto& v:cs) v.resize(sz);
garner(cs,MOD);
return cs[0];
}
vector<int> divide(vector<int> as,vector<int> bs,int MOD){
assert(bs!=vector<int>(bs.size(),0));
assert(as.size()>=bs.size());
int need=as.size()-bs.size()+1;
if(as==vector<int>(as.size(),0)) return {0};
reverse(as.begin(),as.end());
reverse(bs.begin(),bs.end());
while(bs.back()==0){
assert(as.back()==0);
as.pop_back();
bs.pop_back();
}
reverse(as.begin(),as.end());
reverse(bs.begin(),bs.end());
int sz=1;
vector<int> rs({inv(bs[0],MOD)});
while(sz<need){
sz<<=1;
rs=sub(add(rs,rs,MOD),multiply(multiply(rs,rs,MOD),bs,MOD),MOD);
rs.resize(sz);
}
while(as.back()==0) as.pop_back();
while(rs.back()==0) rs.pop_back();
auto cs=multiply(as,rs,MOD);
cs.resize(need,0);
return cs;
}
};
NTT<0> ArbitraryModConvolution::ntt0;
NTT<1> ArbitraryModConvolution::ntt1;
NTT<2> ArbitraryModConvolution::ntt2;
//END CUT HERE
template<typename T,T MOD = 1000000007>
struct Mint{
T v;
Mint():v(0){}
Mint(signed v):v(v){}
Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}
Mint pow(long long k){
Mint res(1),tmp(v);
while(k){
if(k&1) res*=tmp;
tmp*=tmp;
k>>=1;
}
return res;
}
static Mint add_identity(){return Mint(0);}
static Mint mul_identity(){return Mint(1);}
Mint inv(){return pow(MOD-2);}
Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
Mint& operator/=(Mint a){return (*this)*=a.inv();}
Mint operator+(Mint a) const{return Mint(v)+=a;};
Mint operator-(Mint a) const{return Mint(v)-=a;};
Mint operator*(Mint a) const{return Mint(v)*=a;};
Mint operator/(Mint a) const{return Mint(v)/=a;};
Mint operator-() const{return v?Mint(MOD-v):Mint(v);}
bool operator==(const Mint a)const{return v==a.v;}
bool operator!=(const Mint a)const{return v!=a.v;}
bool operator <(const Mint a)const{return v <a.v;}
static vector<Mint> fact,finv,invs;
static void init(int n){
int m=fact.size();
if(n<m) return;
fact.resize(n+1,1);
finv.resize(n+1,1);
invs.resize(n+1,1);
if(m==0) m=1;
for(int i=m;i<=n;i++) fact[i]=fact[i-1]*Mint(i);
finv[n]=Mint(1)/fact[n];
for(int i=n;i>=m;i--) finv[i-1]=finv[i]*Mint(i);
for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];
}
static Mint C(int n,int k){
if(n<k||k<0) return Mint(0);
init(n);
return fact[n]*finv[n-k]*finv[k];
}
static Mint H(int n,int k){
if(n<0||k<0) return Mint(0);
if(!n&&!k) return Mint(1);
init(n+k-1);
return C(n+k-1,k);
}
};
template<typename T,T MOD>
vector<Mint<T, MOD> > Mint<T, MOD>::fact = vector<Mint<T, MOD> >();
template<typename T,T MOD>
vector<Mint<T, MOD> > Mint<T, MOD>::finv = vector<Mint<T, MOD> >();
template<typename T,T MOD>
vector<Mint<T, MOD> > Mint<T, MOD>::invs = vector<Mint<T, MOD> >();
//INSERT ABOVE HERE
signed YUKI_829(){
cin.tie(0);
ios::sync_with_stdio(0);
using ll = long long;
int n,b;
cin>>n>>b;
vector<int> s(n);
for(Int i=0;i<n;i++) cin>>s[i];
using M = Mint<int>;
M::init(3e5);
vector<int> cnt(n,0);
for(int i=0;i<n;i++) cnt[s[i]]++;
using P = pair<int, vector<int> > ;
priority_queue<P> pq;
pq.emplace(-1,vector<int>(1,1));
int sum=0;
for(int i=n-1;i>=0;i--){
if(cnt[i]==0) continue;
M x=M::H(sum,cnt[i]);
M y=M::H(sum+1,cnt[i])-x;
x*=M::fact[cnt[i]];
y*=M::fact[cnt[i]];
pq.emplace(-2,vector<int>({x.v,y.v}));
sum+=cnt[i];
}
const int MOD = 1e9+7;
ArbitraryModConvolution arb;
while(pq.size()>1u){
auto a=pq.top().second;pq.pop();
auto b=pq.top().second;pq.pop();
auto c=arb.multiply(a,b,MOD);
pq.emplace(-(int)c.size(),c);
}
auto dp=pq.top().second;
M ans(0),res(1);
for(int j=0;j<(int)dp.size();j++){
ans+=M((ll)j*(ll)dp[j])*res;
res*=M(b);
}
cout<<ans.v<<endl;
return 0;
}
/*
verified on 2019/06/17
https://yukicoder.me/problems/no/829
*/
signed YUKI_3046(){
cin.tie(0);
ios::sync_with_stdio(0);
int k,n;
cin>>k>>n;
vector<int> xs(n);
for(int i=0;i<n;i++) cin>>xs[i];
const int MOD = 1e9+7;
ArbitraryModConvolution arb;
vector<int> as((1<<17)+k),bs(1<<17);
as[0]=bs[0]=1;
for(int x:xs) bs[x]=MOD-1;
cout<<arb.divide(as,bs,MOD)[k]<<endl;
return 0;
}
/*
verified on 2019/06/29
https://yukicoder.me/problems/no/3046
*/
signed main(){
//YUKI_829();
YUKI_3046();
return 0;
}