結果
問題 | No.1648 Sum of Powers |
ユーザー |
|
提出日時 | 2021-08-13 21:47:39 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 22,252 bytes |
コンパイル時間 | 3,831 ms |
コンパイル使用メモリ | 279,392 KB |
最終ジャッジ日時 | 2025-01-23 18:43:43 |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 6 TLE * 50 |
ソースコード
/*** date : 2021-08-13 21:47:38*/#define NDEBUGusing namespace std;// intrinstic#include <immintrin.h>#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cctype>#include <cfenv>#include <cfloat>#include <chrono>#include <cinttypes>#include <climits>#include <cmath>#include <complex>#include <cstdarg>#include <cstddef>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <deque>#include <fstream>#include <functional>#include <initializer_list>#include <iomanip>#include <ios>#include <iostream>#include <istream>#include <iterator>#include <limits>#include <list>#include <map>#include <memory>#include <new>#include <numeric>#include <ostream>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <streambuf>#include <string>#include <tuple>#include <type_traits>#include <typeinfo>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>// utilitynamespace Nyaan {using ll = long long;using i64 = long long;using u64 = unsigned long long;using i128 = __int128_t;using u128 = __uint128_t;template <typename T>using V = vector<T>;template <typename T>using VV = vector<vector<T>>;using vi = vector<int>;using vl = vector<long long>;using vd = V<double>;using vs = V<string>;using vvi = vector<vector<int>>;using vvl = vector<vector<long long>>;template <typename T, typename U>struct P : pair<T, U> {template <typename... Args>P(Args... args) : pair<T, U>(args...) {}using pair<T, U>::first;using pair<T, U>::second;T &x() { return first; }const T &x() const { return first; }U &y() { return second; }const U &y() const { return second; }P &operator+=(const P &r) {first += r.first;second += r.second;return *this;}P &operator-=(const P &r) {first -= r.first;second -= r.second;return *this;}P &operator*=(const P &r) {first *= r.first;second *= r.second;return *this;}P operator+(const P &r) const { return P(*this) += r; }P operator-(const P &r) const { return P(*this) -= r; }P operator*(const P &r) const { return P(*this) *= r; }};using pl = P<ll, ll>;using pi = P<int, int>;using vp = V<pl>;constexpr int inf = 1001001001;constexpr long long infLL = 4004004004004004004LL;template <typename T>int sz(const T &t) {return t.size();}template <typename T, typename U>inline bool amin(T &x, U y) {return (y < x) ? (x = y, true) : false;}template <typename T, typename U>inline bool amax(T &x, U y) {return (x < y) ? (x = y, true) : false;}template <typename T>inline T Max(const vector<T> &v) {return *max_element(begin(v), end(v));}template <typename T>inline T Min(const vector<T> &v) {return *min_element(begin(v), end(v));}template <typename T>inline long long Sum(const vector<T> &v) {return accumulate(begin(v), end(v), 0LL);}template <typename T>int lb(const vector<T> &v, const T &a) {return lower_bound(begin(v), end(v), a) - begin(v);}template <typename T>int ub(const vector<T> &v, const T &a) {return upper_bound(begin(v), end(v), a) - begin(v);}constexpr long long TEN(int n) {long long ret = 1, x = 10;for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);return ret;}template <typename T, typename U>pair<T, U> mkp(const T &t, const U &u) {return make_pair(t, u);}template <typename T>vector<T> mkrui(const vector<T> &v, bool rev = false) {vector<T> ret(v.size() + 1);if (rev) {for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];} else {for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];}return ret;};template <typename T>vector<T> mkuni(const vector<T> &v) {vector<T> ret(v);sort(ret.begin(), ret.end());ret.erase(unique(ret.begin(), ret.end()), ret.end());return ret;}template <typename F>vector<int> mkord(int N, F f) {vector<int> ord(N);iota(begin(ord), end(ord), 0);sort(begin(ord), end(ord), f);return ord;}template <typename T>vector<int> mkinv(vector<T> &v) {int max_val = *max_element(begin(v), end(v));vector<int> inv(max_val + 1, -1);for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;return inv;}} // namespace Nyaan// bit operationnamespace Nyaan {__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {return _mm_popcnt_u64(a);}inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }template <typename T>inline int gbit(const T &a, int i) {return (a >> i) & 1;}template <typename T>inline void sbit(T &a, int i, bool b) {if (gbit(a, i) != b) a ^= T(1) << i;}constexpr long long PW(int n) { return 1LL << n; }constexpr long long MSK(int n) { return (1LL << n) - 1; }} // namespace Nyaan// inoutnamespace Nyaan {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &... u) {cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &... u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template <typename T, class... U, char sep = ' '>void outr(const T &t, const U &... u) {cout << t;outr(u...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debugnamespace DebugImpl {template <typename U, typename = void>struct is_specialize : false_type {};template <typename U>struct is_specialize<U, typename conditional<false, typename U::iterator, void>::type>: true_type {};template <typename U>struct is_specialize<U, typename conditional<false, decltype(U::first), void>::type>: true_type {};template <typename U>struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {};void dump(const char& t) { cerr << t; }void dump(const string& t) { cerr << t; }void dump(const bool& t) { cerr << (t ? "true" : "false"); }template <typename U,enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>void dump(const U& t) {cerr << t;}template <typename T>void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {string res;if (t == Nyaan::inf) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::inf) res = "-inf";}if constexpr (sizeof(T) == 8) {if (t == Nyaan::infLL) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::infLL) res = "-inf";}}if (res.empty()) res = to_string(t);cerr << res;}template <typename T, typename U>void dump(const pair<T, U>&);template <typename T>void dump(const pair<T*, int>&);template <typename T>void dump(const T& t,enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {cerr << "[ ";for (auto it = t.begin(); it != t.end();) {dump(*it);cerr << (++it == t.end() ? "" : ", ");}cerr << " ]";}template <typename T, typename U>void dump(const pair<T, U>& t) {cerr << "( ";dump(t.first);cerr << ", ";dump(t.second);cerr << " )";}template <typename T>void dump(const pair<T*, int>& t) {cerr << "[ ";for (int i = 0; i < t.second; i++) {dump(t.first[i]);cerr << (i == t.second - 1 ? "" : ", ");}cerr << " ]";}void trace() { cerr << endl; }template <typename Head, typename... Tail>void trace(Head&& head, Tail&&... tail) {cerr << " ";dump(head);if (sizeof...(tail) != 0) cerr << ",";trace(forward<Tail>(tail)...);}} // namespace DebugImpl#ifdef NyaanDebug#define trc(...) \do { \cerr << "## " << #__VA_ARGS__ << " = "; \DebugImpl::trace(__VA_ARGS__); \} while (0)#else#define trc(...) (void(0))#endif// macro#define each(x, v) for (auto&& x : v)#define each2(x, y, v) for (auto&& [x, y] : v)#define all(v) (v).begin(), (v).end()#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)#define reg(i, a, b) for (long long i = (a); i < (b); i++)#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)#define fi first#define se second#define ini(...) \int __VA_ARGS__; \in(__VA_ARGS__)#define inl(...) \long long __VA_ARGS__; \in(__VA_ARGS__)#define ins(...) \string __VA_ARGS__; \in(__VA_ARGS__)#define in2(s, t) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i]); \}#define in3(s, t, u) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i]); \}#define in4(s, t, u, v) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i], v[i]); \}#define die(...) \do { \Nyaan::out(__VA_ARGS__); \return; \} while (0)namespace Nyaan {void solve();}int main() { Nyaan::solve(); }//struct ArbitraryLazyMontgomeryModInt {using mint = ArbitraryLazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static u32 mod;static u32 r;static u32 n2;static u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static void set_mod(u32 m) {assert(m < (1 << 30));assert((m & 1) == 1);mod = m;n2 = -u64(m) % m;r = get_r();assert(r * mod == 1);}u32 a;ArbitraryLazyMontgomeryModInt() : a(0) {}ArbitraryLazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}mint operator+(const mint &b) const { return mint(*this) += b; }mint operator-(const mint &b) const { return mint(*this) -= b; }mint operator*(const mint &b) const { return mint(*this) *= b; }mint operator/(const mint &b) const { return mint(*this) /= b; }bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}mint operator-() const { return mint() - mint(*this); }mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = ArbitraryLazyMontgomeryModInt(t);return (is);}mint inverse() const { return pow(mod - 2); }u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static u32 get_mod() { return mod; }};typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;int64_t mod_sqrt(const int64_t &a, const int64_t &p) {assert(0 <= a && a < p);if (a < 2) return a;using Mint = ArbitraryLazyMontgomeryModInt;Mint::set_mod(p);if (Mint(a).pow((p - 1) >> 1) != 1) return -1;Mint b = 1, one = 1;while (b.pow((p - 1) >> 1) == 1) b += one;int64_t m = p - 1, e = 0;while (m % 2 == 0) m >>= 1, e += 1;Mint x = Mint(a).pow((m - 1) >> 1);Mint y = Mint(a) * x * x;x *= a;Mint z = Mint(b).pow(m);while (y != 1) {int64_t j = 0;Mint t = y;while (t != one) {j += 1;t *= t;}z = z.pow(int64_t(1) << (e - j - 1));x *= z;z *= z;y *= z;e = j;}return x.get();}/*** @brief mod sqrt(Tonelli-Shanks algorithm)* @docs docs/modulo/mod-sqrt.md*/template <typename mint>vector<mint> QuadraticEquation(mint a, mint b, mint c) {assert(mint::get_mod() % 2 != 0);if (a == mint()) {if(b == mint()) {assert(c != mint());return {};}return vector<mint>{-c * b.inverse()};}mint ia = a.inverse(), inv2 = mint(2).inverse();b *= ia, c *= ia;auto D = mod_sqrt(((b * inv2).pow(2) - c).get(), mint::get_mod());if(D == -1) return {};if(D <= 1) return vector<mint>{-b * inv2 + D};return vector<mint>{-b * inv2 + D, -b * inv2 - D};}template <class T>struct Matrix {vector<vector<T> > A;Matrix() = default;Matrix(int n, int m) : A(n, vector<T>(m, T())) {}Matrix(int n) : A(n, vector<T>(n, T())){};int H() const { return A.size(); }int W() const { return A[0].size(); }int size() const { return A.size(); }inline const vector<T> &operator[](int k) const { return A[k]; }inline vector<T> &operator[](int k) { return A[k]; }static Matrix I(int n) {Matrix mat(n);for (int i = 0; i < n; i++) mat[i][i] = 1;return (mat);}Matrix &operator+=(const Matrix &B) {int n = H(), m = W();assert(n == B.H() && m == B.W());for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];return (*this);}Matrix &operator-=(const Matrix &B) {int n = H(), m = W();assert(n == B.H() && m == B.W());for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];return (*this);}Matrix &operator*=(const Matrix &B) {int n = H(), m = B.W(), p = W();assert(p == B.H());vector<vector<T> > C(n, vector<T>(m, T{}));for (int i = 0; i < n; i++)for (int k = 0; k < p; k++)for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];A.swap(C);return (*this);}Matrix &operator^=(long long k) {Matrix B = Matrix::I(H());while (k > 0) {if (k & 1) B *= *this;*this *= *this;k >>= 1LL;}A.swap(B.A);return (*this);}Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }bool operator==(const Matrix &B) const {assert(H() == B.H() && W() == B.W());for (int i = 0; i < H(); i++)for (int j = 0; j < W(); j++)if (A[i][j] != B[i][j]) return false;return true;}bool operator!=(const Matrix &B) const {assert(H() == B.H() && W() == B.W());for (int i = 0; i < H(); i++)for (int j = 0; j < W(); j++)if (A[i][j] != B[i][j]) return true;return false;}friend ostream &operator<<(ostream &os, const Matrix &p) {int n = p.H(), m = p.W();for (int i = 0; i < n; i++) {os << (i ? " " : "") << "[";for (int j = 0; j < m; j++) {os << p[i][j] << (j + 1 == m ? "]\n" : ",");}}return (os);}T determinant() const {Matrix B(*this);assert(H() == W());T ret = 1;for (int i = 0; i < H(); i++) {int idx = -1;for (int j = i; j < W(); j++) {if (B[j][i] != 0) {idx = j;break;}}if (idx == -1) return 0;if (i != idx) {ret *= T(-1);swap(B[i], B[idx]);}ret *= B[i][i];T inv = T(1) / B[i][i];for (int j = 0; j < W(); j++) {B[i][j] *= inv;}for (int j = i + 1; j < H(); j++) {T a = B[j][i];if (a == 0) continue;for (int k = i; k < W(); k++) {B[j][k] -= B[i][k] * a;}}}return ret;}};/*** @brief 行列ライブラリ*/template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = -u64(mod) % mod;static_assert(r * mod == 1, "invalid, r * mod != 1");static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const { return pow(mod - 2); }friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};template <typename mint>std::pair<int, mint> GaussElimination(vector<vector<mint>> &a,int pivot_end = -1,bool diagonalize = false) {int H = a.size(), W = a[0].size();int rank = 0, je = pivot_end;if (je == -1) je = W;mint det = 1;for (int j = 0; j < je; j++) {int idx = -1;for (int i = rank; i < H; i++) {if (a[i][j] != mint(0)) {idx = i;break;}}if (idx == -1) {det = 0;continue;}if (rank != idx) {det = -det;swap(a[rank], a[idx]);}det *= a[rank][j];if (diagonalize && a[rank][j] != mint(1)) {mint coeff = a[rank][j].inverse();for (int k = j; k < W; k++) a[rank][k] *= coeff;}int is = diagonalize ? 0 : rank + 1;for (int i = is; i < H; i++) {if (i == rank) continue;if (a[i][j] != mint(0)) {mint coeff = a[i][j] / a[rank][j];for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;}}rank++;}return make_pair(rank, det);}template <typename mint>vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {int N = a.size();assert(N > 0);assert(N == (int)a[0].size());vector<vector<mint>> m(N, vector<mint>(2 * N));for (int i = 0; i < N; i++) {copy(begin(a[i]), end(a[i]), begin(m[i]));m[i][N + i] = 1;}auto [rank, det] = GaussElimination(m, N, true);if (rank != N) return {};vector<vector<mint>> b(N);for (int i = 0; i < N; i++) {copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));}return b;}//using namespace Nyaan;using mint = LazyMontgomeryModInt<998244353>;// using mint = LazyMontgomeryModInt<1000000007>;using vm = vector<mint>;using vvm = vector<vm>;using namespace Nyaan;void Nyaan::solve() {inl(A,B,P,Q);using mat=Matrix<mint>;mat M(2);M[0][0]=A,M[0][1]=-B,M[1][0]=1;map<vi,int> memo;mat MM;mat S1(2,1);S1[0][0]=A,S1[1][0]=2;mat PQ(2,1);PQ[0][0]=P,PQ[1][0]=Q;{mat a=mat::I(2);rep(i,TEN(5)){auto b=a*S1;vi v(2);v[0]=b[0][0].get(),v[1]=b[1][0].get();memo[v]=i;a*=M;}MM=M;}mat base=mat::I(2);for(int i=0;;i++){if(base.determinant()!=0){mat inv(2);inv.A = inverse_matrix(base.A);mat mt = inv * PQ;vi v(2);v[0]=mt[0][0].get(),v[1]=mt[1][0].get();if(memo.find(v)!=memo.end()){out(i * TEN(5) + memo[v] + 1);exit(0);}}base *= MM;}}