OJ-Problems-Source/HDOJ/5868_zufezzt.cpp

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#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-6;
void File()
{
freopen("D:\\in.txt","r",stdin);
freopen("D:\\out.txt","w",stdout);
}
template <class T>
inline void read(T &x)
{
char c=getchar(); x=0;
while(!isdigit(c)) c=getchar();
while(isdigit(c)) {x=x*10+c-'0'; c=getchar();}
}
LL n,mod=1e9+7;
LL extend_gcd(LL a,LL b,LL &x,LL &y)
{
if(a==0&&b==0) return -1;
if(b==0){x=1;y=0;return a;}
LL d=extend_gcd(b,a%b,y,x);
y-=a/b*x;
return d;
}
LL mod_reverse(LL a,LL n)
{
LL x,y;
LL d=extend_gcd(a,n,x,y);
if(d==1) return (x%n+n)%n;
else return -1;
}
LL phi(LL n)
{
LL res=n,a=n;
for(int i=2;i*i<=a;i++)
{
if(a%i==0)
{
res=res/i*(i-1);
while(a%i==0) a/=i;
}
}
if(a>1) res=res/a*(a-1);
return res;
}
struct Matrix
{
LL A[3][3];
int R, C;
Matrix operator*(Matrix b);
};
Matrix X, Y, Z;
Matrix Matrix::operator*(Matrix b)
{
Matrix c;
memset(c.A, 0, sizeof(c.A));
int i, j, k;
for (i = 1; i <= R; i++)
for (j = 1; j <= b.C; j++)
for (k = 1; k <= C; k++)
c.A[i][j] = (c.A[i][j] + (A[i][k] * b.A[k][j]) % mod) % mod;
c.R = R; c.C = b.C;
return c;
}
void init()
{
memset(X.A, 0, sizeof X.A);
memset(Y.A, 0, sizeof Y.A);
memset(Z.A, 0, sizeof Z.A);
Y.R = 2; Y.C = 2;
for (int i = 1; i <= 2; i++) Y.A[i][i] = 1;
X.R = 2; X.C = 2;
X.A[1][1]=0; X.A[1][2]=1;
X.A[2][1]=1; X.A[2][2]=1;
Z.R = 1; Z.C = 2;
Z.A[1][1]=0; Z.A[1][2]=1;
}
LL work(int x)
{
x--;
while (x)
{
if (x % 2 == 1) Y = Y*X;
x = x >> 1;
X = X*X;
}
Z = Z*Y;
return Z.A[1][2];
}
LL fib(int x)
{
if(x==0) return 0;
init();
return work(x);
}
int main()
{
while(~scanf("%lld",&n))
{
if(n==1) { printf("2\n"); continue; }
LL ans=0;
for(LL i=1;i*i<=n;i++)
{
if(n%i!=0) continue;
LL t=phi(n/i)*((fib(i-1)+fib(i+1))%mod)%mod;
ans=(ans+t)%mod;
if(n/i!=i)
{
t=phi(i)*((fib(n/i-1)+fib(n/i+1))%mod)%mod;
ans=(ans+t)%mod;
}
}
LL ni=mod_reverse(n,mod);
ans=ans*ni%mod;
printf("%lld\n",ans);
}
return 0;
}