196 lines
3.6 KiB
C++
196 lines
3.6 KiB
C++
/* Problem URL: https://codeforces.com/gym/105900/problem/F */
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#include <bits/stdc++.h>
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using namespace std;
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#define V vector
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#define rmin(a, b) a = min(a, b)
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#define rmax(a, b) a = max(a, b)
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#define rep(i, lim) for (int i = 0; i < (lim); i++)
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#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
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#define repv(i, v) for (auto &i : (v))
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#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
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#define sortv(v) sort(v.begin(), v.end())
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#define all(v) (v).begin(), (v).end()
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using vi = vector<int>;
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using vvi = vector<vi>;
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using vvvi = vector<vvi>;
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using vvvvi = vector<vvvi>;
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using ll = long long;
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using vl = vector<ll>;
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using vvl = vector<vl>;
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using vvvl = vector<vvl>;
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using vvvvl = vector<vvvl>;
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template<class v>
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auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
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os << vec[0];
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for (size_t i = 1; i < vec.size(); i++) {
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os << ' ' << vec[i];
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}
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os << '\n';
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return os;
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}
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template<class v>
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auto operator>>(istream &is, vector<v> &vec)->istream& {
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for (auto &i : vec) {
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is >> i;
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}
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return is;
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}
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template<class v>
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auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
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for (auto &i : vec) {
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os << i[0];
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for (size_t j = 1; j < i.size(); j++) {
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os << ' ' << i[j];
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}
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os << '\n';
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}
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return os;
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}
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template<class v>
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auto operator>>(istream &is, vector<vector<v>> &vec)->istream& {
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for (auto &i : vec) {
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for (auto &j : i) {
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is >> j;
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}
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}
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return is;
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}
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template<typename T> tuple<T, T, T> ext_gcd(T a, T b) {
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if (!a) return {b, 0, 1};
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auto [g, x, y] = ext_gcd(b%a, a);
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return {g, y - b/a*x, x};
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}
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template<typename T = ll> struct crt {
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T a, m;
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crt() : a(0), m(1) {}
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crt(T a_, T m_) : a(a_), m(m_) {}
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crt operator * (crt C) {
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auto [g, x, y] = ext_gcd(m, C.m);
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if ((a - C.a) % g) a = -1;
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if (a == -1 or C.a == -1) return crt(-1, 0);
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T lcm = m/g*C.m;
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T ans = a + (x*(C.a-a)/g % (C.m/g))*m;
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return crt((ans % lcm + lcm) % lcm, lcm);
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}
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};
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ll tot(int n) {
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ll ret = n;
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for (int i = 2; i*i <= n; i++) if (n % i == 0) {
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while (n % i == 0) n /= i;
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ret -= ret / i;
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}
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if (n > 1) ret -= ret / n;
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return ret;
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}
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ll fastpow(ll a, ll b, ll tot)
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{
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ll ans = 1;
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ll now = a;
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for (int i = 0; i < 31; i++) {
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if ((b >> i) & 1) {
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ans *= now;
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ans %= tot;
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}
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now *= now;
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now %= tot;
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}
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return ans;
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}
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vvl mul(vvl &a, vvl &b, ll mod)
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{
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vvl ans(a.size(), vl(b[0].size()));
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rep(i, a.size()) {
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rep(j, b[0].size()) {
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rep(k, a[0].size()) {
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ans[i][j] = (ans[i][j] + a[i][k] * b[k][j]) % mod;
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}
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}
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}
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return ans;
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}
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ll binaryexpo(ll pow, ll mod)
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{
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vvl ans = {
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{1, 0},
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{0, 0}
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};
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if (pow <= 1) {
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return pow;
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}
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pow--;
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vvl now = {
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{1, 1},
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{1, 0}
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};
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rep(i, 62) {
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if ((pow >> i) & 1) {
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ans = mul(ans, now, mod);
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}
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now = mul(now, now, mod);
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}
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return ans[0][0];
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}
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ll factor(ll n)
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{
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ll sqr = sqrt(n);
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for (ll i = 2; i <= sqr; i++) {
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if (n % i == 0) {
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return i;
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}
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}
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return n;
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}
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int main()
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{
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ios::sync_with_stdio(false);
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cin.tie(nullptr);
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ll a, b, m;
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cin >> a >> b >> m;
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ll mtot = tot(m);
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if (__gcd(a, m) != 1) {
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ll tmp = factor(mtot);
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crt one(fastpow(a, b, tmp), tmp);
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crt two(fastpow(a, b, mtot / tmp), mtot / tmp);
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mtot = (one * two).m;
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}
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cout << binaryexpo(fastpow(a, b, mtot), m) << '\n';
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}
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