#include #define show(x) cerr << #x << " = " << x << endl using namespace std; using ll = long long; using pii = pair; using vi = vector; template ostream& operator<<(ostream& os, const vector& v) { os << "sz=" << v.size() << "\n["; for (const auto& p : v) { os << p << ","; } os << "]\n"; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } constexpr ll MOD = 1e9 + 7; template constexpr T INF = numeric_limits::max() / 100; ll A, N, M; vector prime; template T extgcd(const T a, const T b, T& x, T& y) // ax+by=gcd(a,b) { T d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } template pair ChineseRemainderTheorem(const pair a1, const pair a2) { assert(gcd(a1.first, a2.first) == 1); const T p1 = a1.first; const T m1 = a1.second; const T p2 = a2.first; const T m2 = a2.second; if (m1 == m2) { return make_pair(p1 * p2, m1); } else { T x, y; extgcd(p1, p2, x, y); assert(p1 * x + p2 * y == 1); x *= (m2 - m1); y *= (m2 - m1); const T p = p1 * p2; return make_pair(p, (((p1 * x + m1) % p) + p) % p); } } int rem(const int n, const int mod) // a↑↑n (mod n) { if (n == 0) { return 1 % mod; } else if (mod == 1) { return 0; } else { int num = mod; vector fac; vector phi; for (const int p : prime) { if (num % p == 0) { int beki = 1; while (num % p == 0) { beki *= p; num /= p; } fac.push_back(make_pair(beki, 1)); phi.push_back(beki / p * (p - 1)); } if (num == 1) { break; } } const int size = fac.size(); for (int i = 0; i < size; i++) { const int m = rem(n - 1, phi[i]); for (int j = 0; j < m; j++) { fac[i].second = (fac[i].second * (A % fac[i].first)) % fac[i].first; } } pair result = fac[0]; for (int i = 1; i < size; i++) { result = ChineseRemainderTheorem(result, fac[i]); } return result.second; } } int main() { cin >> A >> N >> M; vector isprime(M + 1, true); for (int i = 2; i <= M; i++) { if (isprime[i]) { for (int j = 2; i * j <= M; j++) { isprime[i * j] = false; } } } for (int i = 2; i <= M; i++) { if (isprime[i]) { prime.push_back(i); } } cout << rem(N, M) << endl; return 0; }