Cod sursa(job #2955922)

Utilizator nicu_ducalNicu Ducal nicu_ducal Data 18 decembrie 2022 12:10:55
Problema Suma divizorilor Scor 0
Compilator cpp-64 Status done
Runda Arhiva de probleme Marime 2.2 kb
#include <bits/stdc++.h>
using namespace std;

template <typename T> ostream& operator<<(ostream &os, const vector<T> &v) { os << '{'; string sep; for (const auto &x : v) os << sep << x, sep = ", "; return os << '}'; }
template <typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
using i64 = long long int;

const i64 INF = INT_MAX, MOD = 9901;
const double EPS = 1e-9, PI = acos(-1);
const int dx[] = {0, 0, 0, -1, 1, -1, 1, 1, -1};
const int dy[] = {0, -1, 1, 0, 0, -1, 1, -1, 1};

vector<i64> generate_primes(int max_num) {
  vector<i64> primes;
  vector<bool> sieve(max_num + 1, true);
  sieve[0] = sieve[1] = false;
  for (i64 p = 2; p <= max_num; p++) {
    if (not sieve[p]) continue;
    primes.push_back(p);
    for (i64 d = p * 2; d <= max_num; d += p)
      sieve[d] = false;
  }

  return primes;
}

i64 fast_exponentiation(i64 x, i64 n) {
  if (n == 0) return 1;
  if (n == 1) return x % MOD;
  if (n & 1)
    return ((x % MOD) * fast_exponentiation((x * x) % MOD, (n - 1) / 2)) % MOD;
  return fast_exponentiation((x * x) % MOD, n / 2) % MOD;
}

int main() {
  ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
  /// mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

  ifstream cin("sumadiv.in");
  ofstream cout("sumadiv.out");

  i64 A, B; cin >> A >> B;

  vector<i64> primes = generate_primes(1e6 + 5);
  i64 sum = 1;

  for (auto prime: primes) {
    i64 power = 0;
    if (prime * prime > A) break;
    if (A % prime != 0) continue;

    while (A % prime == 0) {
      ++power;
      A /= prime;
    }

    i64 p_pow_d1 = fast_exponentiation(prime, power) % MOD;
    i64 p_pow_Bd1 = fast_exponentiation(p_pow_d1, B) % MOD;
    i64 numerator = ((p_pow_Bd1 * prime) % MOD + MOD - 1) % MOD;
    i64 modinv_denominator = fast_exponentiation(prime - 1, MOD - 2) % MOD;
    sum = (((sum * numerator) % MOD) * modinv_denominator) % MOD;
  }

  if (A > 1) {
    i64 numerator = (fast_exponentiation(A, B + 1) % MOD + MOD - 1) % MOD;
    i64 modinv_denominator = fast_exponentiation(A - 1, MOD - 2) % MOD;
    sum = (((sum * numerator) % MOD) * modinv_denominator) % MOD;
  }

  cout << sum << "\n";

  return 0;
}