// QCFium 法 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; using ull = unsigned long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); int DX[4] = {1, 0, -1, 0}; // 4 近傍(下,右,上,左) int DY[4] = {0, 1, 0, -1}; int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索(昇順) #define repis(i, set) for(int i = lsb(set), bset##i = set; i >= 0; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T getb(T set, int i) { return (set >> i) & T(1); } template inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; //using mint = modint998244353; using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; using pim = pair; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } template inline int lsb(const bitset& b) { return b._Find_first(); } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す #endif // R がバラバラになってしまってた void WA() { int B, C; cin >> B >> C; mint::set_mod(B); vb is_a(B); rep(i, B) is_a[i] = gcd(i, B) == 1; vb is_b(B); rep(i, B) is_b[i] = i % C == 0; dump(is_a); dump(is_b); dsu d(B * B * 2); rep(a, B) { if (!is_a[a]) continue; rep(b, B) { if (!is_b[b]) continue; int i = a * B + b; rep(x, B) rep(y, B) { int j = ((a * x) % B) * B + ((b + a * y) % B); d.merge(i, j); int j2 = ((a * x) % B) * B + ((b + y) % B); d.merge(j2, i); } } } set st; rep(a, B) { if (!is_a[a]) continue; rep(b, B) { if (!is_b[b]) continue; int i = a * B + b; st.insert(d.leader(i)); } } int res = sz(st); if (res >= 100) cout << "100+" << endl; else cout << res << endl; } // サンプル 3 が通らない. void WA2() { auto start = chrono::system_clock::now(); int B, C; cin >> B >> C; mint::set_mod(B); vi as; vector ab; rep(a, B) { if (gcd(a, B) != 1) continue; as.push_back(a); rep(b, B) { if (b % C != 0) continue; ab.push_back({ a, b }); } } dsu d(B * B); mt19937_64 mt((int)time(NULL)); uniform_int_distribution rnd(0, 123456789); while (1) { mint p = as[rnd(mt) % sz(as)]; mint q = rnd(mt) % (B / C) * C; mint r = 0; mint s = 1; mint det = (p * s - q * r); mint det_inv = mint(det).inv(); p *= det_inv; q *= det_inv; // r *= det_inv; // s *= det_inv; for (auto [a, b] : ab) { if (r * ((-1 + a) * p + b * r) == 0 && a * q * r - p * s + b * r * s == -1) { int i = (int)(-q * r + a * p * s + b * r * s).val(); int j = (int)(s * ((-1 + a) * q + b * s)).val(); d.merge(a * B + b, i * B + j); } } auto now = chrono::system_clock::now(); auto msec = chrono::duration_cast(now - start).count(); if (msec >= 3450) break; } set st; rep(a, B) { for (auto [a, b] : ab) { st.insert(d.leader(a * B + b)); } } int res = sz(st); if (res >= 100) cout << "100+" << endl; else cout << res << endl; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); int B, C; cin >> B >> C; mint::set_mod(B); vi as; vi inv(B); rep(a, B) { if (gcd(a, B) != 1) continue; as.push_back(a); inv[a] = (int)(mint(a).inv().val()); } vi bs; rep(b, B) { if (b % C != 0) continue; bs.push_back(b); } dsu d(B * B); repe(a, as) repe(b, bs) repe(p, as) repe(q, bs) { int nb = (b + (a - 1) * q) * inv[p] % B; d.merge(a * B + b, a * B + nb); } dump(d); vi ex(B * B); repe(a, as) repe(b, bs) { ex[d.leader(a * B + b)] = 1; } int res = accumulate(all(ex), 0); dump(res); if (res > 100) EXIT("100+"); cout << res << endl; }