OJ-Problems-Source/HDOJ/3439_autoAC.cpp
2016-09-04 14:10:14 +08:00

131 lines
2.3 KiB
C++

#include<iostream>
#include<cstdio>
#include<string>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long ll;
const int maxn=100005;
ll n,k,m;
ll f1[2*maxn],f2[maxn],c[maxn],mul[maxn],num[maxn],tot;
ll cp()
{
f1[0]=1%m;f1[1]=0;
ll i;
for(i=2;i<=2*m;++i)
f1[i]=(((f1[i-1]+f1[i-2])%m)*(i-1))%m;
return f1[(n-k)%(2*m)];
}
void prem()
{
ll i,mm;
mm=m;
tot=0;
for(i=2;i*i<=mm;++i)
{
if(mm%i==0)
{
c[tot]=i;mul[tot]=1;num[tot]=0;
while(mm%i==0)
{
mul[tot]*=i;
num[tot]++;
mm/=i;
}
tot++;
}
}
if(mm!=1)
{
c[tot]=mm;mul[tot]=mm;num[tot]=1;
tot++;
}
}
ll quickpow(ll a,ll b,ll c)
{
ll ret=1;
while(b)
{
if(b&1)
{
(ret*=a)%=c;
}
(a*=a)%=c;
b>>=1;
}
return ret%c;
}
void ex_gcd(ll a,ll b,ll &x,ll &y)
{
if(b==0)
{
x=1;y=0;
return ;
}
ex_gcd(b,a%b,x,y);
ll t=x;
x=y;
y=t-(a/b)*y;
}
ll count(ll a,ll p)
{
if(a<p)
return 0;
else
return a/p+count(a/p,p);
}
ll count2(ll a,ll p,ll mp)
{
if(a<p)
return f2[a];
return ((f2[a%mp]*quickpow(f2[mp-1],a/mp,mp))%mp*count2(a/p,p,mp))%mp;
}
ll work1(ll id)
{
ll p=c[id];ll mp=mul[id];ll nm=num[id];
ll t1;
t1=count(n,p)-count(k,p)-count(n-k,p);
if(t1>=nm)
return 0;
ll ret=quickpow(p,t1,mp);
ll i,x,y;
f2[0]=1;
for(i=1;i<=mp;++i)
{
f2[i]=f2[i-1];
if(i%p!=0)
f2[i]*=i;
f2[i]%=mp;
}
ex_gcd(count2(k,p,mp)*count2(n-k,p,mp),mp,x,y);
(ret*=x)%=mp;
(ret*=count2(n,p,mp))%=mp;
return ret;
}
ll work()
{
ll i,ret=0,tmp,x,y;
prem();
for(i=0;i<tot;++i)
{
tmp=work1(i);
ex_gcd(m/mul[i],mul[i],x,y);
ret+=(((m/mul[i])%m*x)%m*tmp)%m;
}
ret=(ret%m+m)%m;
return (ret*cp())%m;
}
int main()
{
int t,cas=0;
scanf("%d",&t);
while(t--)
{
cas++;
scanf("%I64d%I64d%I64d",&n,&k,&m);
printf("Case %d: %I64d\n",cas,work());
}
return 0;
}