1054_Efficient_Pseudo_Code.md

Algorithm: Number theory , Inverse Modulo

Problem: 1054 Efficient Pseudo Code

#include <bits/stdc++.h>
using namespace std;
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
//typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds; // find_by_order, order_of_key
#define ll long long
#define vi vector<int>
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vvi vector<vi>
#define vll vector<ll>
#define vvll vector<vector<ll>>
#define vpii vector<pair<int,int>>
#define vpll vector<pair<ll,ll>>
int Set(int N, int pos) {return  N = N | (1<<pos);}
int Reset(int N, int pos) {return  N = N & ~(1<<pos);}
bool Cheek(int N, int pos) {return  (bool)(N & (1<<pos));}
#define least_one_pos(x) __builtin_ffs(x)
#define leading_zeros(x) __builtin_clz(x)
#define tailing_zeros(x) __builtin_ctz(x)
#define num_of_one(x) __builtin_popcount(x)
///............x...........///
#define all(a) a.begin(), a.end()
#define allr(a) a.rbegin(), a.rend()
#define mp(a, b) make_pair(a, b)
#define pb push_back
#define UNIQUE(X) (X).erase(unique(all(X)), (X).end())
#define ft cout << "for test"<<endl;
#define print(v) for (auto it : v)cout << it<<" ";cout << endl;
#define PI acos(-1.0)
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define t_c int test, cs = 1;cin>>test;while (test--)
///................function.....................///

#define mod 1000000007
//........constant........///
const ll N = 1e6+5;
void file(){
   freopen("input.txt","r",stdin);
   freopen("output.txt","w",stdout);
}
ll prime_size=(1<<16);
vll primes;
vector<bool> mark(prime_size);
void sieve(){
    ll i,j;
    mark[0]=mark[1]=1;
    for(i=4; i<prime_size; i+=2)mark[i]=1;
    for(i=3; i*i<=prime_size; i+=2){
        if(!mark[i]){
            for(j=i*i; j<=prime_size; j+=i*2)mark[j]=1;
        }
    }
    primes.pb(2);
    for(i=3; i<=prime_size; i+=2)if(!mark[i])primes.pb(i);
}
long long binpow(long long a, long long b, long long m) {
    a %= m;
    long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a % m;
        a = a * a % m;
        b >>= 1;
    }
    return res;
}
int main(){
    FIO;
    // file();
    sieve();
    t_c{
        ll n,m,i,j;
        cin>>n>>m;
        cout<<"Case "<<cs++<<": ";
        map<ll,ll>pcnt;
        for(auto x:primes){
            if(x*x>n)break;
            if(n%x==0){
                int c=0;
                while(n%x==0){
                    n/=x;
                    c++;
                }
                pcnt[x]=c;
            }
        }
        if(n>1)pcnt[n]=1;
        ll ans=1ll;
        for(auto x:pcnt){
            ll p = x.first;
            ll e = x.second*m;
            ll up = (binpow(p,e+1,mod)-1+mod)%mod;
            ll dwn = binpow(p-1,mod-2,mod);
            ans = ans*(up*dwn%mod)%mod;
        }
        cout<<(ans+mod)%mod<<endl;
    }

}