CF1027G X-mouse in the Campus

#include <bits/stdc++.h>
#define int long long
typedef long long ll;
const int N=1000005;
int m,a[N],f[N],p[N],n,cnt,x,ans;
std::map<int,int> id;
std::vector<int> v;
void init(){
	for (int i=1;i*i<=m;i++)//所有因数 
		if (m%i==0){
			a[++n]=i;
		 	if (m/i!=i) a[++n]=m/i;
		}
	std::sort(a+1,a+n+1);
	for (int i=1;i<=n;i++) id[a[i]]=i;
	int x=m;
	for (int i=2;i*i<=x;i++){
		if (x%i) continue;
		p[++cnt]=i;
		while (x%i==0) x/=i;
	}
	if (x>1) p[++cnt]=x;
	for (int i=1;i<=n;i++) f[i]=m/a[i];
	for (int i=1;i<=cnt;i++)
		for (int j=1;j<=n;j++)
			if (a[j]%p[i]==0)
				f[id[a[j]/p[i]]]-=f[j];
}
ll mul(ll x,ll y,ll mu){
   x%=mu;
   y%=mu;
   ll ans=(x*y-(ll)((double)x*y/mu+0.1)*mu)%mu;
   ans+=ans<0?mu:0;
   return ans;
}
int ksm(int x,int y,int mu){
	int ans=1;
	x=x%mu;
	for (;y;y>>=1,x=mul(x,x,mu))
		if (y&1) ans=mul(x,ans,mu);
	return ans;
}
bool MR(int n){
	if (n==2 || n==3 || n==5 || n==7) return 1;
	if (n%2==0 || n%3==0 || n%5==0 || n%7==0) return 0;
	int T=12;
	int d=n-1,k=0;
	while (d%2==0) d>>=1,k++;
	while (T--){
		int x=rand();
		x=ksm(x,d,n);
		if (x==0) continue;
		for (int i=1;i<=k;i++){
			int t=x;
			x=mul(x,x,n);
			if (x==1 && (t!=1 && t!=n-1)) return 0;
		}
		if (x!=1) return 0;
	}
	return 1;
}
ll gcd(ll x,ll y){
	if (x%y==0) return y;
	return gcd(y,x%y);
}
int PR(int n){
	if (n%2==0) return 2;
	if (n%3==0) return 3;
	int x=rand(),y=x,c=12,step=0,t=1;
	while (++step){
		y=(mul(y,y,n)+c)%n;
		if (x==y) return n;
		ll g=gcd((y-x+n)%n,n);
		if (g>1) return g;
		if (step==t) x=y,t<<=1; 
	}
}
void find(int n){
	if (n==1) return;
	if (MR(n)){
		v.push_back(n);
		return;
	}
	int d=n;
	while (d==n || d==1) d=PR(n);
	while (n%d==0) n/=d;
	find(d);find(n); 
}
signed main(){
	srand(time(0));
	scanf("%lld%lld",&m,&x);
	init();
	for (int i=1;i<n;i++){
		int t=m/a[i],c=f[id[a[i]]];
		v.clear();
		find(c);
		std::sort(v.begin(),v.end());
		std::unique(v.begin(),v.end());
		for (auto j:v)
			while (c%j==0 && ksm(x,c/j,t)==1) c/=j;	
		ans=ans+f[i]/c;
	}
	printf("%lld\n",ans+1);
}