QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#79829 | #2131. Zbiory niezależne [A] | Crysfly | 10 ✓ | 8244ms | 108016kb | C++17 | 6.7kb | 2023-02-20 23:49:56 | 2023-02-20 23:50:00 |
Judging History
answer
// what is matter? never mind.
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
inline int read()
{
char c=getchar();int x=0;bool f=0;
for(;!isdigit(c);c=getchar())f^=!(c^45);
for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
if(f)x=-x;return x;
}
#define mod 998244353
struct modint{
int x;
modint(int o=0){x=o;}
modint &operator = (int o){return x=o,*this;}
modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
modint &operator ^=(int b){
modint a=*this,c=1;
for(;b;b>>=1,a*=a)if(b&1)c*=a;
return x=c.x,*this;
}
modint &operator /=(modint o){return *this *=o^=mod-2;}
friend modint operator +(modint a,modint b){return a+=b;}
friend modint operator -(modint a,modint b){return a-=b;}
friend modint operator *(modint a,modint b){return a*=b;}
friend modint operator /(modint a,modint b){return a/=b;}
friend modint operator ^(modint a,int b){return a^=b;}
friend bool operator ==(modint a,int b){return a.x==b;}
friend bool operator !=(modint a,int b){return a.x!=b;}
bool operator ! () {return !x;}
modint operator - () {return x?mod-x:0;}
bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}
vector<modint> fac,ifac,iv;
inline void initC(int n)
{
if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
int m=iv.size(); ++n;
if(m>=n)return;
iv.resize(n),fac.resize(n),ifac.resize(n);
For(i,m,n-1){
iv[i]=iv[mod%i]*(mod-mod/i);
fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
}
}
inline modint C(int n,int m){
if(m<0||n<m)return 0;
return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}
#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;
#define poly vector<modint>
const modint G=3,Ginv=modint(1)/3;
inline poly one(){poly a;a.push_back(1);return a;}
vector<int>rev;
vector<modint>rts;
inline int ext(int n){
int k=0;
while((1<<k)<n)++k;return k;
}
inline void init(int k){
int n=1<<k;
if(rev.size()==n)return;
rev.resize(n);
For(i,0,n-1)rev[i]=(rev[i>>1]>>1)|((i&1)<<(k-1));
if(rts.size()>=n)return;
int lst=max(1,(int)rts.size()); rts.resize(n);
for(int mid=lst;mid<n;mid<<=1){
modint wn=G^((mod-1)/(mid<<1));
rts[mid]=1;
For(i,1,mid-1)rts[i+mid]=rts[i+mid-1]*wn;
}
}
void ntt(poly&a,int k,int typ)
{
int n=1<<k;
if(typ<0) reverse(a.begin()+1,a.end());
For(i,0,n-1)if(i<rev[i])swap(a[i],a[rev[i]]);
for(int mid=1;mid<n;mid<<=1)
for(int r=mid<<1,j=0;j<n;j+=r)
for(int k=0;k<mid;++k){
modint x=a[j+k],y=rts[mid+k]*a[j+k+mid];
a[j+k]=x+y,a[j+k+mid]=x-y;
}
if(typ<0){
modint inv=modint(1)/n;
For(i,0,n-1)a[i]*=inv;
}
}
poly operator +(poly a,poly b){
int n=max(a.size(),b.size());a.resize(n),b.resize(n);
For(i,0,n-1)a[i]+=b[i];return a;
}
poly operator -(poly a,poly b){
int n=max(a.size(),b.size());a.resize(n),b.resize(n);
For(i,0,n-1)a[i]-=b[i];return a;
}
poly operator *(poly a,modint b){
int n=a.size();
For(i,0,n-1)a[i]*=b;return a;
}
poly operator *(modint b,poly a){
int n=a.size();
For(i,0,n-1)a[i]*=b;return a;
}
poly operator *(poly a,poly b){
if(!a.size()||!b.size())return {};
if((int)a.size()<=32 || (int)b.size()<=32){
poly c(a.size()+b.size()-1,0);
for(int i=0;i<a.size();++i)
for(int j=0;j<b.size();++j)
c[i+j]+=a[i]*b[j];
return c;
}
int n=(int)a.size()+(int)b.size()-1,k=ext(n);
a.resize(1<<k),b.resize(1<<k),init(k);
ntt(a,k,1),ntt(b,k,1);
For(i,0,(1<<k)-1)a[i]*=b[i];
ntt(a,k,-1),a.resize(n);return a;
}
poly Tmp;
poly pmul(poly a,poly b,int n,bool ok=0)
{
int k=ext(n); init(k);
a.resize(1<<k),ntt(a,k,1);
if(!ok) b.resize(1<<k),ntt(b,k,1),Tmp=b;
For(i,0,(1<<k)-1)a[i]*=Tmp[i];
ntt(a,k,-1),a.resize(n);
return a;
}
poly inv(poly a,int n)
{
a.resize(n);
if(n==1){
poly f(1,1/a[0]);
return f;
}
poly f0=inv(a,(n+1)>>1),f=f0;
poly now=pmul(a,f0,n,0);
for(int i=0;i<f0.size();++i)now[i]=0;
now=pmul(now,poly(0),n,1);
f.resize(n);
for(int i=f0.size();i<n;++i)f[i]=-now[i];
return f;
}
poly inv(poly a){return inv(a,a.size());}
poly deriv(poly a){
int n=(int)a.size()-1;
For(i,0,n-1)a[i]=a[i+1]*(i+1);
a.resize(n);return a;
}
poly inter(poly a){
int n=a.size()+1;a.resize(n);
Rep(i,n-1,1)a[i]=a[i-1]/i;
a[0]=0;return a;
}
poly ln(poly a){
int n=a.size();
a=inter(deriv(a)*inv(a));
a.resize(n);return a;
}
poly exp(poly a,int k){
int n=1<<k;a.resize(n);
if(n==1)return one();
poly f0=exp(a,k-1);f0.resize(n);
return f0*(one()+a-ln(f0));
}
poly exp(poly a){
int n=a.size();
a=exp(a,ext(n));a.resize(n);return a;
}
#define maxn 1000005
#define inf 0x3f3f3f3f
modint c;
poly g,h,eg;
poly get(poly f,int n){
poly res(n,0);
f.resize(n);
For(i,2,n-1)
for(int j=0;i*j<n;++j)
res[j*i]+=iv[i]*f[j];
return res;
}
poly mulx(poly f){
int n=f.size(); f.resize(n+1);
Rep(i,n,1)f[i]=f[i-1]; f[0]=0; return f;
}
void solve(int mx){
g={0},h={0},eg={1};
for(int n=2;n<=mx;n<<=1){
poly a=get(g+h,n);
poly b=get(g,n);
g.resize(n),h.resize(n);
poly C=mulx({c});
// cout<<"n: "<<n<<endl;
// for(auto x:a)cout<<x.x<<" ";cout<<"\n";
// for(auto x:b)cout<<x.x<<" ";cout<<"\n";
poly ex1=exp(b+g);
poly ex2=exp(g+a);
poly ex3=C*ex1; ex3.resize(n); ex3=exp(ex3);
poly qwq=mulx(ex1)*c; qwq.resize(n); // qwq = c*x*e^{g+b}
poly up=c*ex2*ex3-c*ex1-g; up.resize(n);
poly dw=ex3*(C*c*ex1*ex2+c*ex2);
dw=dw-c*ex1;
dw[0]-=1; dw.resize(n);
// for(auto x:up)cout<<x.x<<" ";cout<<"\n";
// for(auto x:dw)cout<<x.x<<" ";cout<<"\n";
poly res=g-up*inv(dw); res.resize(n);
// poly chk=c*exp(a+res+C*exp(b+res))-c*exp(b+res); chk.resize(n);
// for(auto x:chk)cout<<x.x<<" "; cout<<" chk\n";
// for(auto x:res)cout<<x.x<<" "; cout<<" res\n";
g=res;
h=mulx(exp(b+g))*c; h.resize(n);
// for(auto x:g)cout<<x.x<<" ";puts("");
// for(auto x:h)cout<<x.x<<" ";puts("");
}
}
poly sq(poly f){
int n=f.size();
poly res(n);
For(i,0,n-1)if(i%2==0)res[i]=f[i/2];
return res;
}
poly divx(poly f){
int n=f.size();
assert(f[0].x==0);
For(i,0,n-2)f[i]=f[i+1];
f.resize(n-1);
return f;
}
signed main()
{
initC(1<<20);
int l=read(),r=read();
int n=1<<ext(r+2);
c=read();
solve(n);
poly res=g+h;
res=res-g*h;
res=res+((mod+1)/2)*(sq(g)-g*g);
res=res+((mod+1)/2)*divx(sq(h)-h*h);
res.resize(n);
// for(auto x:res)cout<<x.x<<" ";
modint out=0;
For(i,l,r)out+=res[i];
cout<<out.x;
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 1
Accepted
Test #1:
score: 1
Accepted
time: 23ms
memory: 15208kb
input:
1 3 1
output:
9
result:
ok single line: '9'
Test #2:
score: 0
Accepted
time: 11ms
memory: 15300kb
input:
1 3 2
output:
149
result:
ok single line: '149'
Test #3:
score: 0
Accepted
time: 15ms
memory: 15336kb
input:
1 1 1
output:
2
result:
ok single line: '2'
Test #4:
score: 0
Accepted
time: 20ms
memory: 15300kb
input:
1 8 1
output:
5227
result:
ok single line: '5227'
Test #5:
score: 0
Accepted
time: 12ms
memory: 15340kb
input:
3 8 1
output:
5223
result:
ok single line: '5223'
Subtask #2:
score: 1
Accepted
Test #6:
score: 1
Accepted
time: 22ms
memory: 15340kb
input:
80 80 1
output:
812033063
result:
ok single line: '812033063'
Test #7:
score: 0
Accepted
time: 19ms
memory: 15336kb
input:
78 78 1
output:
182498472
result:
ok single line: '182498472'
Test #8:
score: 0
Accepted
time: 11ms
memory: 15296kb
input:
75 75 1
output:
617232937
result:
ok single line: '617232937'
Subtask #3:
score: 1
Accepted
Test #9:
score: 1
Accepted
time: 65ms
memory: 16196kb
input:
3000 3000 1
output:
316190887
result:
ok single line: '316190887'
Test #10:
score: 0
Accepted
time: 58ms
memory: 16216kb
input:
2836 2836 1
output:
78805654
result:
ok single line: '78805654'
Subtask #4:
score: 1
Accepted
Test #11:
score: 1
Accepted
time: 208ms
memory: 18228kb
input:
10000 10000 737697546
output:
662262394
result:
ok single line: '662262394'
Test #12:
score: 0
Accepted
time: 222ms
memory: 18324kb
input:
9692 9692 521790758
output:
688689567
result:
ok single line: '688689567'
Subtask #5:
score: 1
Accepted
Test #13:
score: 1
Accepted
time: 911ms
memory: 26884kb
input:
46264 60000 823824735
output:
279507395
result:
ok single line: '279507395'
Test #14:
score: 0
Accepted
time: 906ms
memory: 26888kb
input:
40971 58765 596622251
output:
519148445
result:
ok single line: '519148445'
Subtask #6:
score: 1
Accepted
Test #15:
score: 1
Accepted
time: 1850ms
memory: 38108kb
input:
1315 120000 1
output:
400606029
result:
ok single line: '400606029'
Test #16:
score: 0
Accepted
time: 1877ms
memory: 38108kb
input:
65583 118765 1
output:
930420532
result:
ok single line: '930420532'
Subtask #7:
score: 1
Accepted
Test #17:
score: 1
Accepted
time: 3938ms
memory: 61760kb
input:
250000 250000 485195676
output:
723474605
result:
ok single line: '723474605'
Test #18:
score: 0
Accepted
time: 3851ms
memory: 61820kb
input:
234567 234567 549849068
output:
674655026
result:
ok single line: '674655026'
Subtask #8:
score: 1
Accepted
Test #19:
score: 1
Accepted
time: 3870ms
memory: 61728kb
input:
124158 250000 526698216
output:
401019144
result:
ok single line: '401019144'
Test #20:
score: 0
Accepted
time: 3863ms
memory: 61752kb
input:
164096 244921 299495732
output:
460839141
result:
ok single line: '460839141'
Subtask #9:
score: 1
Accepted
Test #21:
score: 1
Accepted
time: 7995ms
memory: 107916kb
input:
500000 500000 504789929
output:
821656212
result:
ok single line: '821656212'
Test #22:
score: 0
Accepted
time: 8048ms
memory: 108016kb
input:
489127 489127 612302745
output:
411092702
result:
ok single line: '411092702'
Subtask #10:
score: 1
Accepted
Test #23:
score: 1
Accepted
time: 8244ms
memory: 107932kb
input:
482751 500000 921732625
output:
368107184
result:
ok single line: '368107184'
Test #24:
score: 0
Accepted
time: 8225ms
memory: 107936kb
input:
55889 499999 19705394
output:
706108398
result:
ok single line: '706108398'