Cod sursa(job #2956014)

Utilizator nicu_ducalNicu Ducal nicu_ducal Data 18 decembrie 2022 15:14:39
Problema Suma divizorilor Scor 100
Compilator cpp-64 Status done
Runda Arhiva de probleme Marime 1.89 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<pair<i64, i64>> decompose(i64 a, i64 b) {
  vector<pair<i64, i64>> factorization;
  for (int p = 2; p * p <= a; ++p) {
    if (a % p != 0) continue;

    i64 d = 0;
    while (a % p == 0) {
      d += b;
      a /= p;
    }

    factorization.emplace_back(p, d);
  }

  if (a > 1) {
    factorization.emplace_back(a, b);
  }

  return factorization;
}

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("sumdiv.in");
  ofstream cout("sumdiv.out");

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

  i64 sum = 1;
  vector<pair<i64, i64>> factorization = decompose(A, B);
  for (auto &it: factorization) {
    i64 prime = it.first, expo = it.second;

    if (prime % MOD != 1) {
      i64 numerator = (fast_exponentiation(prime, expo + 1) % MOD - 1 + MOD) % MOD;
      i64 modinv_denominator = fast_exponentiation(prime - 1, MOD - 2) % MOD;
      sum = (((sum * numerator) % MOD) * modinv_denominator) % MOD;
    } else {
      sum = (sum * (expo + 1)) % MOD;
    }
  }

  cout << sum << "\n";

  return 0;
}