Mathematics - Number Theory - Generalized Euler descending (template)

Unused Euler screen:

Euler descending less suitable number of computations.

#include <bits/stdc++.h>
#define ll long long
using namespace std;
ll a,m,b;

inline ll read(ll m){
    register ll x=0,f=0;char ch=getchar();
    while(!isdigit(ch)) ch=getchar();
    while(isdigit(ch)){
        x=x*10+ch-'0';
        if(x>=m) f=1;
        x%=m;ch=getchar();
    }
    return x+(f==1?m:0);
}

ll phi(ll n){
    ll ans=n,m=sqrt(n);
    for(ll i=2;i<=m;i++){
        if(n%i==0){
            ans=ans/i*(i-1);
            while(n%i==0) n/=i; 
        }
    }
    if(n>1) ans=ans/n*(n-1);
    return ans;
}

ll fast_pow(ll a,ll b,ll p){
    ll ret=1;
    for(;b;b>>=1,a=a*a%p)
        if(b&1) ret=ret*a%p;
    return ret;
}

int main()
{
    scanf("%lld%lld",&a,&m);
    b=read(phi(m));
    printf("%lld\n",fast_pow(a,b,m));
    return 0;
}

Using a linear sieve optimized because the array can not open too restricted, it must be less than 1e8 MOD

#include <bits/stdc++.h>
#define ll long long
#define maxn 10000000 
using namespace std;
bool ok[maxn];
int prime[maxn],phi[maxn],cnt;
ll a,m,b;
void sieve()
{ 
        phi[1]=1;
	for(ll i=2;i<maxn;++i)
	{
		if(!ok[i])
		{
			prime[cnt++]=i;
			phi[i]=i-1;
		}
		for(int j=0;j<cnt;++j)
		{
			if(i*prime[j]>=maxn)break;
			ok[i*prime[j]]=1;
			if(i%prime[j]==0)
			{
				phi[i*prime[j]]=phi[i]*prime[j];//prime[j]是i的因子 prime[j]的素因子项包含在i的素因子项里
				break; 
			}
			else phi[i*prime[j]]=phi[i]*(prime[j]-1);//prime[j]与i互质 phi[i*prime[j]=phi[i]*phi[prime[j]]
		}
	}
}
inline ll read(ll m){
    register ll x=0,f=0;char ch=getchar();
    while(!isdigit(ch)) ch=getchar();
    while(isdigit(ch)){
        x=x*10+ch-'0';
        if(x>=m) f=1;
        x%=m;ch=getchar();
    }
    return x+(f==1?m:0);
}

ll fast_pow(ll a,ll b,ll p){
    ll ret=1;
    for(;b;b>>=1,a=a*a%p)
        if(b&1) ret=ret*a%p;
    return ret;
}

int main()
{
    sieve();
    scanf("%lld%lld",&a,&m);
    b=read(phi[m]);
    printf("%lld\n",fast_pow(a,b,m));
    return 0;
}