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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#382284#8568. Expected DiameterCrysflyAC ✓3974ms56964kbC++177.1kb2024-04-08 10:55:362024-04-08 10:55:37

Judging History

你现在查看的是最新测评结果

  • [2024-04-08 10:55:37]
  • 评测
  • 测评结果:AC
  • 用时:3974ms
  • 内存:56964kb
  • [2024-04-08 10:55:36]
  • 提交

answer

#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)
#define ull unsigned long long
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,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	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;
int rts[2100000];
inline int ext(int n){
	int k=0;
	while((1<<k)<n)++k;return k; 
}
inline void init(int k){
	int n=1<<k;
	rts[0]=1,rts[1<<k]=qpow(31,1<<(21-k)).x;
	Rep(i,k,1)rts[1<<(i-1)]=1ull*rts[1<<i]*rts[1<<i]%mod;
	For(i,1,n-1)rts[i]=1ull*rts[i&(i-1)]*rts[i&-i]%mod;
}

void ntt(poly&a,int k,int typ){
	int n=1<<k;
	static ull tmp[2100000];
	for(int i=0;i<n;++i)tmp[i]=a[i].x;
	if(typ==1){
		for(int l=n>>1;l>=1;l>>=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod*(*g)%mod;
					x[l]=*x+mod-o,*x+=o;
				}
			}
		}
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod;
	}else{
		for(int l=1;l<n;l<<=1){
			ull*k=tmp;
			for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
				for(ull*x=k;x<k+l;++x){
					int o=x[l]%mod;
					x[l]=(*x+mod-o)*(*g)%mod,*x+=o;
				}
			}
		}
		int iv=qpow(n,mod-2).x;
		for(int i=0;i<n;++i)a[i].x=tmp[i]%mod*iv%mod;
		reverse(a.begin()+1,a.end());
	}
}
 
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 *(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);
	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);
	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); initC(n);
	Rep(i,n-1,1)a[i]=a[i-1]*iv[i];
	a[0]=0;return a;
}
poly ln(poly a){
	int n=a.size();
	a=deriv(a)*inv(a),a.resize(n-1);return inter(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;
}
poly div(poly a,poly b){
	int n=a.size(),m=b.size(),k=ext(n-m+1);
	reverse(a.begin(),a.end()),reverse(b.begin(),b.end());
	a.resize(n-m+1),b.resize(n-m+1);
	a=a*inv(b),a.resize(n-m+1),reverse(a.begin(),a.end()); return a;
}
poly modulo(poly a,poly b){
	if(b.size()>a.size())return a;
	int n=b.size()-1;
	a=a-div(a,b)*b;a.resize(n);return a;
}

#define maxn 200005
#define inf 0x3f3f3f3f

int n;
modint p1,p2;
poly g[2005],h[2005],h2[2005];

signed main()
{
	n=read(); initC(n+5);
	modint X=read(),Y=read();
	p1=X/Y,p2=1-p1;
	if(n==1){
		puts("0");
		exit(0);
	}
	init(19);
	g[0].resize(n+1),g[0][1]=1;
	h[0]=g[0];
	For(i,1,n){
		if(i==1) g[i]=exp(g[i-1]*p1);
		else g[i]=exp(g[i-1]*p1+g[i-2]*p2);
		g[i].insert(g[i].begin(),0);
		g[i].resize(n+1);
		h[i]=g[i]-g[i-1];
	//	For(j,0,n) cout<<(g[i][j]*fac[j]).x<<" "; cout<<" g\n";
	//	For(j,0,n) cout<<(h[i][j]*fac[j]).x<<" "; cout<<" h\n";
	}
//	exit(0);
	modint res=0;
	// on edge
	For(i,0,n){
	//	poly ans=h[i]*h[i];
//		modint add=ans[n]*((mod+1)/2);
	//	cout<<"ans: "<<i*2+1<<" "<<add.x<<"\n";
		modint add=0;
		For(j,0,n) add+=h[i][j]*h[i][n-j];
		add*=((mod+1)/2);
	//	cout<<"ans_2 "<<i<<" "<<add.x<<"\n";
		add*=(i*2+(p1+p2*2));
		res+=add;
		
		if(i){
			// (i-1) - 2 - i
			add=0;
			For(j,0,n) add+=h[i][j]*h[i-1][n-j];
			add*=(i*2+1)*p2;
			res+=add;
		}
	}
//	cout<<"res "<<(res*fac[n]).x<<"\n";
//	puts("QAQ");
	// on point
	For(i,1,n){
		poly hh=h[i-1]*p1;
		if(i>=2) hh=hh+h[i-2]*p2;
		
	//	poly tmp=(exp(hh)-one()-hh);
		
		poly tmp=exp(hh);
		tmp=tmp-one()-hh;
		
	//	tmp=(exp(h[i-1]*p1)-one()-(h[i-1]*p1));
		tmp.resize(n+1);
//		For(j,0,n)cout<<(hh[j]*fac[j]).x<<" "; cout<<" hh\n";
//		if(i>=2 && p2.x) {
//			poly t2=(exp(h[i-2]*p2)-one()-(h[i-2]*p2));
//			for(auto x:t2)cout<<x.x<<" "; cout<<"t2\n";
//			tmp=tmp*t2;
//		}
		
	//	tmp=tmp*g[i-1];
	//	cout<<"SZ "<<g[i-1].size()<<" "<<tmp.size()<<"\n";
//		For(j,0,n) cout<<(tmp[j]*fac[j]).x<<" "; cout<<" tmp\n";
		modint add=0;
		For(j,0,n) add+=tmp[j]*g[i-1][n-j];
//		cout<<"Ans "<<i*2<<" "<<add.x<<"\n";
		res+=add*(i*2);
	}
	res*=fac[n];
//	cout<<"res "<<res.x<<"\n"; 
	res/=qpow(n,n-2);
	cout<<res.x;
	return 0;
}
/*
1 2 3
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 8700kb

input:

2 1 3

output:

665496237

result:

ok 1 number(s): "665496237"

Test #2:

score: 0
Accepted
time: 0ms
memory: 9000kb

input:

3 2 3

output:

665496238

result:

ok 1 number(s): "665496238"

Test #3:

score: 0
Accepted
time: 3967ms
memory: 56176kb

input:

2000 1 2

output:

254870088

result:

ok 1 number(s): "254870088"

Test #4:

score: 0
Accepted
time: 3970ms
memory: 56912kb

input:

2000 1 3

output:

193693601

result:

ok 1 number(s): "193693601"

Test #5:

score: 0
Accepted
time: 3974ms
memory: 56964kb

input:

1999 188 211

output:

463395288

result:

ok 1 number(s): "463395288"

Test #6:

score: 0
Accepted
time: 3962ms
memory: 56852kb

input:

1990 470 818

output:

479264654

result:

ok 1 number(s): "479264654"

Test #7:

score: 0
Accepted
time: 948ms
memory: 21588kb

input:

1000 407 783

output:

20089106

result:

ok 1 number(s): "20089106"

Test #8:

score: 0
Accepted
time: 940ms
memory: 21456kb

input:

990 884 901

output:

94051884

result:

ok 1 number(s): "94051884"

Test #9:

score: 0
Accepted
time: 942ms
memory: 20660kb

input:

995 873 988

output:

209191626

result:

ok 1 number(s): "209191626"

Test #10:

score: 0
Accepted
time: 233ms
memory: 10908kb

input:

500 307 938

output:

603465152

result:

ok 1 number(s): "603465152"

Test #11:

score: 0
Accepted
time: 229ms
memory: 11940kb

input:

490 237 732

output:

402554558

result:

ok 1 number(s): "402554558"

Test #12:

score: 0
Accepted
time: 232ms
memory: 12028kb

input:

495 473 511

output:

833418554

result:

ok 1 number(s): "833418554"

Test #13:

score: 0
Accepted
time: 55ms
memory: 9688kb

input:

250 69 207

output:

786182422

result:

ok 1 number(s): "786182422"

Test #14:

score: 0
Accepted
time: 56ms
memory: 10128kb

input:

240 184 259

output:

473414786

result:

ok 1 number(s): "473414786"

Test #15:

score: 0
Accepted
time: 54ms
memory: 10372kb

input:

245 478 807

output:

312847415

result:

ok 1 number(s): "312847415"

Test #16:

score: 0
Accepted
time: 17ms
memory: 9972kb

input:

125 112 253

output:

31497383

result:

ok 1 number(s): "31497383"

Test #17:

score: 0
Accepted
time: 16ms
memory: 10084kb

input:

120 137 498

output:

923043504

result:

ok 1 number(s): "923043504"

Test #18:

score: 0
Accepted
time: 13ms
memory: 8116kb

input:

100 230 792

output:

203877027

result:

ok 1 number(s): "203877027"

Extra Test:

score: 0
Extra Test Passed