Cod sursa(job #2685263)

Utilizator SochuDarabaneanu Liviu Eugen Sochu Data 16 decembrie 2020 14:18:01
Problema Suma si numarul divizorilor Scor 70
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 1.61 kb
#include <bits/stdc++.h>
#define FastIO ios_base::sync_with_stdio(false) , cin.tie(0) , cout.tie(0)
#define FILES freopen("ssnd.in" , "r" , stdin) , freopen("ssnd.out" , "w" , stdout)
#define ll long long

using namespace std;

const ll N = 1e6;
const ll M = 9973;

ll x;
bitset < N / 2 + 10> ciur;
vector < ll > pr;

ll Pw(ll n , ll p)
{
    ll ans = 1;

    for( ; p ; p >>= 1 , n = 1ll * n * n % M)
        if(p & 1)
            ans = 1ll * ans * n % M;

    return ans;
}

void prec()
{
    ll i , j;

    for(i = 1 ; ((i * i) << 1) + (i << 1) <= N ; i++)
        if(!ciur[i])
            for(j = ((i * i) << 1) + (i << 1) ; (j << 1) + 1 <= N ; j += (i << 1) + 1)
                ciur[j] = 1;

    pr.push_back(2);

    for(i = 1 ; (i << 1) + 1 <= N ; i++)
        if(ciur[i] == 0)
            pr.push_back(i * 2 + 1);
}

pair < ll , ll > solve(ll x)
{
    ll e , i;
    ll card = 1;
    ll sum = 1;

    for(i = 0 ; i < pr.size() && pr[i] <= x ; i++)
        if(x % pr[i] == 0)
        {
           e = 0;

            while(x % pr[i] == 0)
                ++e , x /= pr[i];

            card *= e + 1;
            sum = sum * (Pw(pr[i] , e + 1) - 1) % M * Pw(pr[i] - 1 , M - 2) % M;
        }

    if(x > 1)
        card *= 2 , sum = sum * Pw(x , 2) % M * Pw((x - 1) , M - 2) % M;

    return {card , sum};
}

signed main()
{
	#ifndef ONLINE_JUDGE
		FastIO , FILES;
	#endif

    prec();

    ll q; cin >> q;
    while(q--)
    {
        cin >> x;
        pair < ll , ll > s = solve(x);
        cout << s.first << ' ' << s.second << '\n';
    }

    return 0;
}