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Cod sursa(job #639623)
#include<cstdio>
#define MOD 9999991;
long long c[1000011],ex[2000011],i,n,j,p;
using namespace std;
int exp(int pr,int n)
{
long long put,sum;
put=pr;
sum=0;
while (n/put>0)
{
sum=sum+n/put;
put*=pr;
}
return sum;
}
int pow(int f,int p)
{
int aux;
if (p==0) return 1;
else if(p%2==0)
{
aux=pow(f,p/2);
return (aux*aux)%MOD;
}
else return f*pow(f,p-1)%MOD;
}
int main()
{
freopen("dirichlet.in","r",stdin);
freopen("dirichlet.out","w",stdout);
int nr=0;
scanf("%d",&n);
for(i=2;i<2*n;i++)
{
bool ok;
ok=true;
for(j=1;j<=nr&&c[j]*c[j]<=i;j++)
if (i%c[j]==0)
ok=false;
if (ok)
{
nr++;
c[nr]=i;
}
}
for(i=1;i<=nr;i++)
{
ex[c[i]]=(exp(c[i],2*n)-exp(c[i],n)-exp(c[i],n+1))%MOD;
}
p=1;
for(i=1;i<=nr;i++)
{
if (ex[c[i]]!=0)
p=(p*pow(c[i],ex[c[i]]))%MOD;
}
printf("%d\n",p);
}