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#722270#9612. 月亮的背面是粉红色的Larunatrecy100 ✓1592ms495596kbC++149.7kb2024-11-07 18:24:212024-11-07 18:24:21

Judging History

你现在查看的是最新测评结果

  • [2024-11-07 18:24:21]
  • 评测
  • 测评结果:100
  • 用时:1592ms
  • 内存:495596kb
  • [2024-11-07 18:24:21]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
using u32 = int32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;

using ci = const int;

typedef unsigned long long ull;
typedef __uint128_t L;
struct FastMod {
    ull b, m;
    FastMod(ull b) : b(b), m(ull((L(1) << 64) / b)) {}
    ull red(ull a) {
        ull q = (ull)((L(m) * a) >> 64);
        ull r = a - q * b; // can be proven that 0 <= r < 2*b
        return r >= b ? r - b : r;
    }
}P(1);
const int mod = 1e9+7;
inline int mul(int x,int y){return P.red(1ll*x*y);}
inline int add(int x,int y){return x+y>=mod?x+y-mod:x+y;}
inline int sub(int x,int y){return x-y<0?x-y+mod:x-y;}
typedef long long LL;
struct Fact {
	i64 x, y;
	Fact() : x(0), y(0) {}
	Fact(i64 _x, i64 _y) : x(_x), y(_y) {}
	inline Fact operator+(const Fact &o) const {
		return Fact(x + o.x, y + o.y);
	}
};
const int N = 1e7+7;
int vi[N],prime[N],tot=0,pc[N],F[N],s[N],mu[N];
int m,K;
struct info
{
    int w[2];
}S[N],Mu[N];
void init(int n)
{
    s[1]=1;mu[1]=1;F[1]=1;
    for(int i=2;i<=n;i++)
    {
        if(!vi[i])
        {
            vi[i]=i;
            prime[++tot]=i;
            mu[i]=mod-1;
            F[i]=2;s[i]=2;pc[i]=2;
        }
        for(int j=1;j<=tot;j++)
        {
            if(prime[j]>vi[i]||1ll*i*prime[j]>n)break;
            int k=i*prime[j];
            vi[k]=prime[j];
            if(i%prime[j]==0)
            {
                pc[k]=pc[i]+1;
                s[k]=s[i]/pc[i]*pc[k];
                pc[k]=pc[i]+1;
                F[k]=F[i];
                break;
            }
            s[k]=s[i]*2;
            pc[k]=2;
            mu[k]=mod-mu[i];
            F[k]=F[i]*2;
        }
    }
    for(int i=1;i<=n;i++)
    {
        S[i].w[0]=add(S[i-1].w[0],s[i]);
        Mu[i].w[0]=add(Mu[i-1].w[0],mu[i]);
        S[i].w[1]=add(S[i-1].w[1],mul(s[i],i));
        Mu[i].w[1]=add(Mu[i-1].w[1],1ll*mu[i]*mul(i,i)%mod);
    }
}
typedef long long LL;
struct val
{
    int w[3][3];
    void clr()
    {
        w[1][0]=w[0][1]=w[1][1]=w[2][0]=w[0][2]=0;
    }
};
int G[20][20],B[20],C[20][20],inv[20];
inline int sign(int x){return (x&1)?mod-1:1;}
void prework()
{
    int n=10;
    inv[1]=1;
    for(int i=2;i<=n;i++)
    inv[i]=1ll*inv[mod%i]*(mod-mod/i)%mod;
    B[0]=1;
    C[0][0]=1;
    for(int i=1;i<=n;i++)
    {
        C[i][0]=1;
        for(int j=1;j<=i;j++)
        C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
    }
    for(int i=1;i<=n;i++)
    for(int j=0;j<=i-1;j++)
    B[i]=(B[i]-1ll*C[i][j]*B[j]%mod*inv[i-j+1]%mod+mod)%mod;
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<=i;j++)
        G[i][i+1-j]=1ll*inv[i+1]*sign(j)%mod*C[i+1][j]%mod*B[j]%mod;
    }
}
inline int Sum0(int n){return n;}
inline int Sum1(int n){return P.red(1ll*P.red(1ll*n*(n+1))*inv[2]);}
inline int Sum2(int n){return P.red(1ll*P.red(1ll*n*(n+1))*P.red(1ll*(2*n+1)*inv[6]));}
inline int Sum3(int n){int v=P.red(1ll*P.red(1ll*n*(n+1))*inv[2]);return P.red(1ll*v*v);}
inline int Sumk(int n,int k)
{
    if(k==0)return n;
    if(k==1)return P.red(1ll*P.red(1ll*n*(n+1))*inv[2]);
    if(k==2)return P.red(1ll*P.red(1ll*n*(n+1))*P.red(1ll*(2*n+1)*inv[6]));
    int v=P.red(1ll*P.red(1ll*n*(n+1))*inv[2]);
    return P.red(1ll*v*v);
}
int tmpa[10],tmpb[10];
int R,tmp[10];
typedef unsigned long long ULL;
int test=0;
i128 Val[3][3];
val mapa[3000000];
void solo(int x)
{
    mapa[x].w[1][1]=Val[1][1]%mod;Val[1][1]=0;
    mapa[x].w[0][1]=Val[0][1]%mod;Val[0][1]=0;
    mapa[x].w[1][0]=Val[1][0]%mod;Val[1][0]=0;
    mapa[x].w[2][0]=Val[2][0]%mod;Val[2][0]=0;
    mapa[x].w[0][2]=Val[0][2]%mod;Val[0][2]=0;
}
int Test=0;
unordered_map<ULL,int> id;
int idx=0;
void euclid(LL A,LL B)
{
    while(B)
    {
        if(B>=A)
        {
            B%=A;
        }
        else swap(A,B);
    }
}
namespace H
{
    struct edge
    {
        LL A,B;
        int next,id;
    }e[3000200];
    const int M = 2e7+3;
    int link[M],t=0;
    void ins(LL A,LL B,int id)
    {
        int x=(A%M*13331%M+B*131%M)%M;
        e[++t].A=A;
        e[t].B=B;
        e[t].id=id;
        e[t].next=link[x];
        link[x]=t;
    }
    int qry(LL A,LL B)
    {
        int x=(A%M*13331%M+B*131%M)%M;
        for(int i=link[x];i;i=e[i].next)
        if(e[i].A==A&&e[i].B==B)return e[i].id;
        return -1;
    }
}
int Euclid(LL A,LL B)
{
    if(!B)return 0;
    int d=H::qry(A,B);
    if(d!=-1)return d;
    int x=++idx;H::ins(A,B,x);
    ++Test;
    if(B>=A)
    {
        int y=Euclid(A,B%A);
        int c=(B/A)%mod,u=(A%mod);
        tmp[1]=Sum1(u);tmp[2]=Sum2(u);tmp[3]=Sum3(u);
        for(int p=0;p<=R;p++)
        {
            if(p>0)
            {
                Val[p][0]+=mapa[y].w[p][0];
                Val[p][0]+=1ll*c*tmp[p+1];
            }
            if(R-p>=1)
            {
                Val[p][1]+=mapa[y].w[p][1];
                Val[p][1]+=(i128)c*mapa[y].w[p+1][0];
                Val[p][1]+=(i128)G[1][1]*c*tmp[p+1];
                Val[p][1]+=(i128)G[1][2]*c*c%mod*tmp[p+2];
            }
            if(R-p>=2)
            {
                Val[p][2]+=mapa[y].w[p][2];
                Val[p][2]+=(i128)c*mapa[y].w[1][1]*2;
                Val[p][2]+=(i128)c*c*mapa[y].w[2][0];
                Val[p][2]+=(i128)G[2][1]*c*tmp[1];
                Val[p][2]+=(i128)G[2][2]*c*c%mod*tmp[2];
                Val[p][2]+=(i128)G[2][3]*c*c*c%mod*tmp[3];
            }
        }
        solo(x);
        return x;
    }
    int y=Euclid(B,A);
    int u=(A%mod),v=(B%mod);
    tmpa[0]=tmpb[0]=1;
    tmpa[0]=Sum0(u);tmpb[0]=Sum0(v);
    tmpa[1]=Sum1(u);tmpb[1]=Sum1(v);
    tmpa[2]=Sum2(u);tmpb[2]=Sum2(v);
    Val[1][0]=1ll*tmpa[1]*tmpb[0]-mapa[y].w[0][1]+u;
    Val[0][1]=1ll*tmpa[0]*tmpb[1]-mapa[y].w[1][0]+v;
    Val[1][1]=1ll*tmpa[1]*tmpb[1]-mapa[y].w[1][1]+1ll*u*v;
    Val[2][0]=1ll*tmpa[2]*tmpb[0]-mapa[y].w[0][2]+1ll*u*u;
    Val[0][2]=1ll*tmpa[0]*tmpb[2]-mapa[y].w[2][0]+1ll*v*v;
    solo(x);
    return x;
}
i128 Ret[5];
info ask(LL n)
{
    Ret[0]=Ret[1]=0;
    if(n<=K)return S[n];
	const int Q = cbrt(n);
	LL B=sqrt(n),x=n/B,y=B+1;
	static vector<Fact> q;
	q.push_back(Fact(1, 0));
	q.push_back(Fact(1, 1));
	auto ck=[&n](LL x,LL y) {return n<x*y;};
	auto judge=[&n](LL x,Fact v) {return i128(n)*v.x<=i128(x)*x*v.y;};
	while(1)
    {
		Fact L=q.back();q.pop_back();
		Fact R=q.back(),M;
        int u=Euclid(L.x,L.y);
		while(ck(x+L.x,y-L.y))
		{
			Ret[0] += x * L.y + (L.y + 1) * (L.x - 1) / 2;
		    Ret[1]+=(i128)(Sum1((x-1)%mod))*(Sum1(y-1)-Sum1(y-L.y-1));
		    LL x0=x+L.x,y0=y-L.y;
		    Ret[1]+=(i128)x0*mapa[u].w[0][1];
		    Ret[1]-=(i128)y0*(mapa[u].w[1][0]+Sum1(P.red(L.x)));
            Ret[1]-=mapa[u].w[1][1];
            Ret[1]+=(i128)x0*y0*((L.y + 1)*(L.x+1)/2+1);
            Ret[1]-=(i128)x*y;
            Ret[1]-=(i128)(x+L.x)*(y-L.y);
			x+=L.x,y-=L.y;
		}
		if (y <= Q) break;
		while (!ck(x + R.x, y - R.y)) {
			L = R;
			q.pop_back();
			R = q.back();
		}
		while (1) {
			M = L + R;
			if (ck(x + M.x, y - M.y)) q.push_back(R = M);
			else {
				if (judge(x + M.x, R)) break;
				L = M;
			}
		}
	}
	for (int i = 1; i < y; ++i)
    {
        Ret[0]+=(n/i);
        Ret[1]+=1ll*i*Sum1((n/i)%mod);
    }
    Ret[0]=Ret[0]*2-1ll*B*B;
    Ret[1]=Ret[1]*2-1ll*Sum1(B)*Sum1(B);
    Ret[0]=(Ret[0]%mod+mod)%mod;
    Ret[1]=(Ret[1]%mod+mod)%mod;
    info ret;ret.w[0]=Ret[0];ret.w[1]=Ret[1];
    return ret;
}
unordered_map<LL,info> vis;
info Sum(LL n)
{
    if(n<=K)return Mu[n];
    if(vis.find(n)!=vis.end())return vis[n];
    i128 w0=1,w1=1;
    LL l=2,r=n;
    for(;l<=n;l=r+1)
    {
        r=(n/(n/l));
        info W=Sum(n/l);
        w0-=1ll*(Sum0(r%mod)-Sum0((l-1)%mod))*W.w[0];
        w1-=1ll*(Sum2(r%mod)-Sum2((l-1)%mod))*W.w[1];
    }
    info ret=(info){(w0%mod+mod)%mod,(w1%mod+mod)%mod};
    return vis[n]=ret;
}
LL ask0(LL n)
{
	i128 res=0;
    if(n<=K)return S[n].w[0];
	const int Q = cbrt(n);
	LL B=sqrt(n),x=n/B,y=B+1;
	static vector<Fact> q;
	q.push_back(Fact(1, 0));
	q.push_back(Fact(1, 1));
	auto ck=[&n](LL x,LL y) {return n<x*y;};
	auto judge=[&n](LL x,Fact v) {return i128(n)*v.x<=i128(x)*x*v.y;};
	while(1)
    {
		Fact L=q.back();q.pop_back();
		Fact R=q.back(),M;
		while(ck(x+L.x,y-L.y))
		{
			res+=x * L.y + (L.y + 1) * (L.x - 1) / 2;
			x+=L.x,y-=L.y;
		}
		if (y <= Q) break;
		while (!ck(x + R.x, y - R.y)) {
			L = R;
			q.pop_back();
			R = q.back();
		}
		while (1) {
			M = L + R;
			if (ck(x + M.x, y - M.y)) q.push_back(R = M);
			else {
				if (judge(x + M.x, R)) break;
				L = M;
			}
		}
	}
	for (int i = 1; i < y; ++i)res+=(n/i);
	res%=mod;res=res*2-B*B%mod;res=(res%mod+mod)%mod;
	return res%mod;
}
LL Ans[10];
int main()
{
    //freopen("Sum.in","r",stdin);
    //freopen("Sum.out","w",stdout);
    LL n,tp;
    cin>>n>>tp;
    if(n>=1e13)K=1e7;
    else K=1e6;
    prework();
    m=1;P=FastMod(mod);init(K);R=2;
    if(tp==0)
    {
	    LL l=1,r;
	    for(;l*l<=n;l=r+1)
	    {
	        r=sqrt(n/(n/(l*l)));
	        if(l==r&&r<=K&&mu[l]==0);
	        else
	        {
	            info R=Sum(r),L=Sum(l-1);
				LL W=ask0(n/(l*l));
	            Ans[0]+=1ll*(R.w[0]-L.w[0])*W%mod;
	        }
	    }
	    Ans[0]%=mod;
	    Ans[0]=(Ans[0]%mod+mod)%mod;
	    cout<<1ll*Ans[0]*Ans[0]%mod;
	    return 0;
	}
    LL l=1,r;
    for(;l*l<=n;l=r+1)
    {
        r=sqrt(n/(n/(l*l)));
        if(l==r&&r<=K&&mu[l]==0);
        else
        {
            info R=Sum(r),L=Sum(l-1),W=ask(n/(l*l));
            Ans[0]+=1ll*(R.w[0]-L.w[0])*W.w[0]%mod;
            Ans[1]+=1ll*(R.w[1]-L.w[1])*W.w[1]%mod;
        }
    }
    Ans[0]%=mod;Ans[1]%=mod;
    cout<<1ll*Ans[0]*Ans[0]%mod<<' '<<1ll*Ans[1]*Ans[1]%mod<<endl;
	return 0;
}

詳細信息

Subtask #1:

score: 3
Accepted

Test #1:

score: 3
Accepted
time: 19ms
memory: 54648kb

input:

1726 1

output:

84290761 74619067

result:

ok 2 number(s): "84290761 74619067"

Test #2:

score: 3
Accepted
time: 21ms
memory: 52932kb

input:

3608 1

output:

433014481 672891299

result:

ok 2 number(s): "433014481 672891299"

Test #3:

score: 3
Accepted
time: 16ms
memory: 54468kb

input:

2921 1

output:

271096225 547734266

result:

ok 2 number(s): "271096225 547734266"

Subtask #2:

score: 3
Accepted

Test #4:

score: 3
Accepted
time: 15ms
memory: 58024kb

input:

6116899 1

output:

219318963 301450440

result:

ok 2 number(s): "219318963 301450440"

Test #5:

score: 3
Accepted
time: 17ms
memory: 56228kb

input:

6260707 1

output:

148720176 263856753

result:

ok 2 number(s): "148720176 263856753"

Test #6:

score: 3
Accepted
time: 11ms
memory: 59308kb

input:

6763677 1

output:

944542490 136397156

result:

ok 2 number(s): "944542490 136397156"

Subtask #3:

score: 8
Accepted

Test #7:

score: 8
Accepted
time: 19ms
memory: 53828kb

input:

6469467712 0

output:

147393348

result:

ok 1 number(s): "147393348"

Test #8:

score: 8
Accepted
time: 17ms
memory: 52796kb

input:

8967004453 0

output:

229436583

result:

ok 1 number(s): "229436583"

Test #9:

score: 8
Accepted
time: 11ms
memory: 50656kb

input:

6636594384 0

output:

995965072

result:

ok 1 number(s): "995965072"

Subtask #4:

score: 8
Accepted

Test #10:

score: 8
Accepted
time: 11ms
memory: 70732kb

input:

8292948816 1

output:

566765721 287485757

result:

ok 2 number(s): "566765721 287485757"

Test #11:

score: 8
Accepted
time: 25ms
memory: 69604kb

input:

8592748771 1

output:

649470692 164561252

result:

ok 2 number(s): "649470692 164561252"

Test #12:

score: 8
Accepted
time: 23ms
memory: 69204kb

input:

9827380808 1

output:

291159931 188690805

result:

ok 2 number(s): "291159931 188690805"

Subtask #5:

score: 8
Accepted

Test #13:

score: 8
Accepted
time: 75ms
memory: 109804kb

input:

900472451132 1

output:

247050500 963765719

result:

ok 2 number(s): "247050500 963765719"

Test #14:

score: 8
Accepted
time: 58ms
memory: 110944kb

input:

850862494659 1

output:

200210720 915108650

result:

ok 2 number(s): "200210720 915108650"

Test #15:

score: 8
Accepted
time: 51ms
memory: 116288kb

input:

851346512859 1

output:

895785763 504512885

result:

ok 2 number(s): "895785763 504512885"

Subtask #6:

score: 10
Accepted

Test #16:

score: 10
Accepted
time: 169ms
memory: 142304kb

input:

9864907300784 1

output:

359943536 720268421

result:

ok 2 number(s): "359943536 720268421"

Test #17:

score: 10
Accepted
time: 144ms
memory: 136224kb

input:

8181674676063 1

output:

839993102 994056029

result:

ok 2 number(s): "839993102 994056029"

Test #18:

score: 10
Accepted
time: 182ms
memory: 143076kb

input:

9893510217522 1

output:

157499971 930653488

result:

ok 2 number(s): "157499971 930653488"

Subtask #7:

score: 13
Accepted

Test #19:

score: 13
Accepted
time: 340ms
memory: 362164kb

input:

96735749745529 0

output:

223354886

result:

ok 1 number(s): "223354886"

Test #20:

score: 13
Accepted
time: 347ms
memory: 361468kb

input:

95243570720799 0

output:

555372474

result:

ok 1 number(s): "555372474"

Test #21:

score: 13
Accepted
time: 341ms
memory: 361904kb

input:

97668723090105 0

output:

84562124

result:

ok 1 number(s): "84562124"

Subtask #8:

score: 14
Accepted

Test #22:

score: 14
Accepted
time: 617ms
memory: 462460kb

input:

94060593399194 1

output:

52991150 887133157

result:

ok 2 number(s): "52991150 887133157"

Test #23:

score: 14
Accepted
time: 666ms
memory: 462084kb

input:

98527940728119 1

output:

281611635 910356955

result:

ok 2 number(s): "281611635 910356955"

Test #24:

score: 14
Accepted
time: 656ms
memory: 461368kb

input:

90501814019947 1

output:

666385143 229785369

result:

ok 2 number(s): "666385143 229785369"

Subtask #9:

score: 16
Accepted

Test #25:

score: 16
Accepted
time: 1153ms
memory: 361832kb

input:

9772457586483846 0

output:

631039552

result:

ok 1 number(s): "631039552"

Test #26:

score: 16
Accepted
time: 1122ms
memory: 361428kb

input:

9889806164705403 0

output:

169322134

result:

ok 1 number(s): "169322134"

Test #27:

score: 16
Accepted
time: 1138ms
memory: 361640kb

input:

9422498258316766 0

output:

413943782

result:

ok 1 number(s): "413943782"

Test #28:

score: 16
Accepted
time: 1124ms
memory: 360256kb

input:

9845978636381962 0

output:

857401052

result:

ok 1 number(s): "857401052"

Test #29:

score: 16
Accepted
time: 1130ms
memory: 360904kb

input:

9761171951453691 0

output:

205712009

result:

ok 1 number(s): "205712009"

Test #30:

score: 16
Accepted
time: 1113ms
memory: 361404kb

input:

9224667465673566 0

output:

143979878

result:

ok 1 number(s): "143979878"

Subtask #10:

score: 17
Accepted

Test #31:

score: 17
Accepted
time: 1553ms
memory: 495152kb

input:

949243849085176 1

output:

508465534 771553755

result:

ok 2 number(s): "508465534 771553755"

Test #32:

score: 17
Accepted
time: 1547ms
memory: 494232kb

input:

924225524519163 1

output:

867410272 870831653

result:

ok 2 number(s): "867410272 870831653"

Test #33:

score: 17
Accepted
time: 1592ms
memory: 495596kb

input:

978079151303393 1

output:

235076358 675828942

result:

ok 2 number(s): "235076358 675828942"

Test #34:

score: 17
Accepted
time: 1579ms
memory: 494176kb

input:

929804617107620 1

output:

790604296 73162158

result:

ok 2 number(s): "790604296 73162158"

Test #35:

score: 17
Accepted
time: 1550ms
memory: 494668kb

input:

989806727450552 1

output:

378550840 783149232

result:

ok 2 number(s): "378550840 783149232"