結果
問題 | No.1648 Sum of Powers |
ユーザー |
![]() |
提出日時 | 2021-08-13 22:42:51 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 22,326 bytes |
コンパイル時間 | 1,881 ms |
コンパイル使用メモリ | 156,076 KB |
最終ジャッジ日時 | 2025-01-23 20:25:34 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 42 WA * 14 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end());return vec; }template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']';return os; }#if __cplusplus >= 201703Ltemplate <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); returnis; }template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }#endiftemplate <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ',';os << '}'; return os; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os;}template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')';return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp)os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET <<endl#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ <<COLOR_RESET << endl : cerr)#else#define dbg(x) (x)#define dbgif(cond, x) 0#endiftemplate <int md> struct ModInt {#if __cplusplus >= 201402L#define MDCONST constexpr#else#define MDCONST#endifusing lint = long long;MDCONST static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val;MDCONST ModInt() : val(0) {}MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }MDCONST ModInt(lint v) { _setval(v % md + md); }MDCONST explicit operator bool() const { return val != 0; }MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }friend MDCONST ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv() % md);}MDCONST bool operator==(const ModInt &x) const { return val == x.val; }MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }MDCONST ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static std::vector<ModInt> facs, facinvs, invs;MDCONST static void _precalculation(int N) {int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}MDCONST lint inv() const {if (this->val < std::min(md >> 1, 1 << 21)) {while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val].val;} else {return this->pow(md - 2).val;}}MDCONST ModInt fac() const {while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val];}MDCONST ModInt facinv() const {while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val];}MDCONST ModInt doublefac() const {lint k = (this->val + 1) / 2;return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}MDCONST ModInt nCr(const ModInt &r) const {return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();}MDCONST ModInt nPr(const ModInt &r) const {return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();}ModInt sqrt() const {if (val == 0) return 0;if (md == 2) return val;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, md - x.val));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;// Calculate log_A B (MOD M) (baby-step gian-step)// DiscreteLogarithm dl(M, A);// lint ans = dl.log(B);// Complexity: O(M^(1/2)) for each query// Verified: <https://judge.yosupo.jp/problem/discrete_logarithm_mod>// Constraints: 0 <= A < M, B < M, 1 <= M <= 1e9 (M is not limited to prime)struct DiscreteLogarithm {using lint = long long int;int M, stepsize;lint baby_a, giant_a, g;std::unordered_map<lint, int> baby_log_dict;lint inverse(lint a) {lint b = M / g, u = 1, v = 0;while (b) {lint t = a / b;a -= t * b;std::swap(a, b);u -= t * v;std::swap(u, v);}u %= M / g;return u >= 0 ? u : u + M / g;}DiscreteLogarithm(int mod, int a_new) : M(mod), baby_a(a_new % mod), giant_a(1) {g = 1;while (std::__gcd(baby_a, M / g) > 1) g *= std::__gcd(baby_a, M / g);stepsize = 32; // lg(MAX_M)while (stepsize * stepsize < M / g) stepsize++;lint now = 1 % (M / g), inv_g = inverse(baby_a);for (int n = 0; n < stepsize; n++) {if (!baby_log_dict.count(now)) baby_log_dict[now] = n;(now *= baby_a) %= M / g;(giant_a *= inv_g) %= M / g;}}// log(): returns the smallest nonnegative x that satisfies a^x = b mod M, or -1 if there's no solutionlint log(lint b) {b %= M;lint acc = 1 % M;for (int i = 0; i < stepsize; i++) {if (acc == b) return i;(acc *= baby_a) %= M;}if (b % g) return -1; // No solutionlint now = b * giant_a % (M / g);for (lint q = 1; q <= M / stepsize + 1; q++) {if (baby_log_dict.count(now)) return q * stepsize + baby_log_dict[now];(now *= giant_a) %= M / g;}return -1;}};template <typename T> struct matrix {int H, W;std::vector<T> elem;typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }inline T &at(int i, int j) { return elem[i * W + j]; }inline T get(int i, int j) const { return elem[i * W + j]; }int height() const { return H; }int width() const { return W; }std::vector<std::vector<T>> vecvec() const {std::vector<std::vector<T>> ret(H);for (int i = 0; i < H; i++) {std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));}return ret;}operator std::vector<std::vector<T>>() const { return vecvec(); }matrix() = default;matrix(int H, int W) : H(H), W(W), elem(H * W) {}matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));}static matrix Identity(int N) {matrix ret(N, N);for (int i = 0; i < N; i++) ret.at(i, i) = 1;return ret;}matrix operator-() const {matrix ret(H, W);for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];return ret;}matrix operator*(const T &v) const {matrix ret = *this;for (auto &x : ret.elem) x *= v;return ret;}matrix operator/(const T &v) const {matrix ret = *this;const T vinv = T(1) / v;for (auto &x : ret.elem) x *= vinv;return ret;}matrix operator+(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];return ret;}matrix operator-(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];return ret;}matrix operator*(const matrix &r) const {matrix ret(H, r.W);for (int i = 0; i < H; i++) {for (int k = 0; k < W; k++) {for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);}}return ret;}matrix &operator*=(const T &v) { return *this = *this * v; }matrix &operator/=(const T &v) { return *this = *this / v; }matrix &operator+=(const matrix &r) { return *this = *this + r; }matrix &operator-=(const matrix &r) { return *this = *this - r; }matrix &operator*=(const matrix &r) { return *this = *this * r; }bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }bool operator<(const matrix &r) const { return elem < r.elem; }matrix pow(int64_t n) const {matrix ret = Identity(H);bool ret_is_id = true;if (n == 0) return ret;for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {if (!ret_is_id) ret *= ret;if ((n >> i) & 1) ret *= (*this), ret_is_id = false;}return ret;}std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {matrix x = *this;while (n) {if (n & 1) vec = x * vec;x *= x;n >>= 1;}return vec;};matrix transpose() const {matrix ret(W, H);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);}return ret;}// Gauss-Jordan elimination// - Require inverse for every non-zero element// - Complexity: O(H^2 W)template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {int piv = -1;for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j;}return piv;}template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c)) return j;}return -1;}matrix gauss_jordan() const {int c = 0;matrix mtr(*this);std::vector<int> ws;ws.reserve(W);for (int h = 0; h < H; h++) {if (c == W) break;int piv = choose_pivot(mtr, h, c);if (piv == -1) {c++;h--;continue;}if (h != piv) {for (int w = 0; w < W; w++) {std::swap(mtr[piv][w], mtr[h][w]);mtr.at(piv, w) *= -1; // To preserve sign of determinant}}ws.clear();for (int w = c; w < W; w++) {if (mtr.at(h, w) != 0) ws.emplace_back(w);}const T hcinv = T(1) / mtr.at(h, c);for (int hh = 0; hh < H; hh++)if (hh != h) {const T coeff = mtr.at(hh, c) * hcinv;for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;mtr.at(hh, c) = 0;}c++;}return mtr;}int rank_of_gauss_jordan() const {for (int i = H * W - 1; i >= 0; i--) {if (elem[i]) return i / W + 1;}return 0;}T determinant_of_upper_triangle() const {T ret = 1;for (int i = 0; i < H; i++) ret *= get(i, i);return ret;}int inverse() {assert(H == W);std::vector<std::vector<T>> ret = Identity(H), tmp = *this;int rank = 0;for (int i = 0; i < H; i++) {int ti = i;while (ti < H and tmp[ti][i] == 0) ti++;if (ti == H) {continue;} else {rank++;}ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);T inv = T(1) / tmp[i][i];for (int j = 0; j < W; j++) ret[i][j] *= inv;for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;for (int h = 0; h < H; h++) {if (i == h) continue;const T c = -tmp[h][i];for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;}}*this = ret;return rank;}friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {assert(m.W == int(v.size()));std::vector<T> ret(m.H);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];}return ret;}friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {assert(int(v.size()) == m.H);std::vector<T> ret(m.W);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);}return ret;}std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }friend std::ostream &operator<<(std::ostream &os, const matrix &x) {os << "[(" << x.H << " * " << x.W << " matrix)";os << "\n[column sums: ";for (int j = 0; j < x.W; j++) {T s = 0;for (int i = 0; i < x.H; i++) s += x.get(i, j);os << s << ",";}os << "]";for (int i = 0; i < x.H; i++) {os << "\n[";for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";os << "]";}os << "]\n";return os;}friend std::istream &operator>>(std::istream &is, matrix &x) {for (auto &v : x.elem) is >> v;return is;}};// Example: Fibonacci numbers f(n) = af(n - 1) + bf(n - 2)// (a = b = 1): 0=>1, 1=>1, 2=>2, 3=>3, 4=>5, ...template <typename T> T Fibonacci(long long int k, int a = 1, int b = 1) {matrix<T> mat(2, 2);mat[0][1] = 1;mat[1][0] = b;mat[1][1] = a;return mat.pow(k + 1)[0][1];}int main() {mint A, B, P, Q;cin >> A >> B >> P >> Q;if (B == 0) {DiscreteLogarithm dl(mint::mod(), A.val);cout << dl.log(P.val) << '\n';return 0;}mint A2 = A * A - B * 2;// if (A2 == mint(P)) {// puts("2");// return 0;// }const int D = 201010;map<mint, lint> shift;shift[P] = 0;shift[Q] = 1;const mint Binv = B.inv();FOR(t, 2, D + 10) {mint R = (Q * A - P) * Binv;if (R == A) {// cout << t + 1 << '\n';// return 0;}if (!shift.count(R)) shift[R] = t;P = Q;Q = R;}matrix<mint> trans(2, 2);trans[0][0] = A;trans[0][1] = -B;trans[1][0] = 1;trans = trans.pow(D);mint h0 = A, h1 = A2;for (lint jump = 0, i0 = 1;; jump++, i0 += D) {if (shift.count(h0)) {cout << i0 + shift[h0] << '\n';return 0;}vector<mint> v{h1, h0};v = trans * v;h1 = v[0], h0 = v[1];}}