#include #include #include #define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i)) #define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i)) #define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i)) #define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i)) #define ALL(x) begin(x), end(x) using ll = long long; using namespace std; /** * @note O(\sqrt{n}) * @note about 1.0 sec for 10^5 queries with n < 10^10 */ struct prepared_primes { int size; vector sieve; vector primes; prepared_primes(int size_) : size(size_) { sieve.resize(size); REP3 (p, 2, size) if (sieve[p] == 0) { primes.push_back(p); for (int k = p; k < size; k += p) { if (sieve[k] == 0) { sieve[k] = p; } } } } vector prime_factorize(ll n) { assert (1 <= n and n < (ll)size * size); vector result; // trial division for large part for (int p : primes) { if (n < size or n < (ll)p * p) { break; } while (n % p == 0) { n /= p; result.push_back(p); } } // small part if (n == 1) { // nop } else if (n < size) { while (n != 1) { result.push_back(sieve[n]); n /= sieve[n]; } } else { result.push_back(n); } assert (is_sorted(ALL(result))); return result; } vector list_all_factors(ll n) { auto p = prime_factorize(n); vector d; d.push_back(1); for (int l = 0; l < p.size(); ) { int r = l + 1; while (r < p.size() and p[r] == p[l]) ++ r; int n = d.size(); REP (k1, r - l) { REP (k2, n) { d.push_back(d[d.size() - n] * p[l]); } } l = r; } return d; } }; int solve(int n, int k, int m) { prepared_primes primes(sqrt(n) + 100); auto factors = primes.list_all_factors(n); sort(ALL(factors)); __gnu_pbds::gp_hash_table cur, prv; cur.insert(1); while (k -- and cur.size() != prv.size()) { cur.swap(prv); for (int d1 : prv) for (int d2 : factors) { if ((ll)d1 * d2 > m) break; cur.insert(d1 * d2); } } return cur.size(); } int main() { int n, k, m; cin >> n >> k >> m; cout << solve(n, k, m) << endl; return 0; }