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Cod sursa(job #734357)
#include<fstream>
#define int1 long long
#define nmax 2000000000
using namespace std;
ifstream fin("inversmodular.in");
ofstream fout("inversmodular.out");
int1 N , A, i, j, k, ret;
bool v[100000];
int a[100000];
int1 di[10000],p;
int1 rid( int1 A, int1 fi )
{
int1 t;
if(fi == 1)
return A % ret ;
if(fi % 2 == 0)
{
t = rid(A, fi/2) % ret;
return t * t % ret;
}
else
return rid(A, fi-1) % ret * A %ret;
}
void read()
{
int1 s = 0, semn = 1, sp =0, fi;
fin >> A >> N;
ret = N;
for( i = 2; i <= 100000 - 1; i++)
{
for( j = i + i ; j <= 100000 - 1; j += i )
v[j] = 1;
}
for( i = 2; i<= 100000 - 1; i++)
{
if(!v[i])
a[++k] = i;
}
k = 1 ;
while(N>1)
{
if(N % a[k] == 0)
{
di[++p] = a[k];
while(N % a[k] == 0)
{
N /= a[k];
}
}
k++;
}
for( i = 1; i< 1<<p ; i++ )
{
semn = -1;
sp = 0;
for( j = 0 ; j < p; j++)
{
if(i & 1<< j)
{
semn *= (-1);
sp += ret / di[j+1] ;
}
}
s += sp * semn;
}
fi = ret - s - 1 ;
//fout<< fi <<'\n';
fout << rid(A, fi) % ret;
}
int main()
{
read();
fin.close();
fout.close();
return 0;
}