結果
問題 | No.2188 整数列コイントスゲーム |
ユーザー | hitonanode |
提出日時 | 2023-01-13 21:48:59 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 3 ms / 2,000 ms |
コード長 | 31,962 bytes |
コンパイル時間 | 4,436 ms |
コンパイル使用メモリ | 248,580 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-12-24 17:06:04 |
合計ジャッジ時間 | 6,623 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
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testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 3 ms
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testcase_02 | AC | 2 ms
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testcase_03 | AC | 2 ms
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testcase_04 | AC | 2 ms
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testcase_05 | AC | 2 ms
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testcase_06 | AC | 2 ms
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testcase_07 | AC | 2 ms
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testcase_08 | AC | 2 ms
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testcase_09 | AC | 2 ms
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testcase_10 | AC | 3 ms
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testcase_11 | AC | 2 ms
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testcase_12 | AC | 2 ms
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testcase_13 | AC | 2 ms
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testcase_14 | AC | 2 ms
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testcase_15 | AC | 2 ms
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testcase_16 | AC | 2 ms
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testcase_17 | AC | 2 ms
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testcase_18 | AC | 2 ms
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testcase_19 | AC | 2 ms
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testcase_20 | AC | 2 ms
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testcase_21 | AC | 2 ms
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testcase_22 | AC | 2 ms
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testcase_23 | AC | 2 ms
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testcase_24 | AC | 2 ms
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testcase_25 | AC | 3 ms
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testcase_26 | AC | 2 ms
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testcase_27 | AC | 3 ms
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testcase_28 | AC | 2 ms
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testcase_29 | AC | 3 ms
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testcase_30 | AC | 3 ms
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testcase_31 | AC | 2 ms
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testcase_32 | AC | 2 ms
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testcase_33 | AC | 2 ms
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testcase_34 | AC | 3 ms
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testcase_35 | AC | 2 ms
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testcase_36 | AC | 3 ms
5,248 KB |
testcase_37 | AC | 2 ms
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testcase_38 | AC | 2 ms
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testcase_39 | AC | 2 ms
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testcase_40 | AC | 2 ms
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testcase_41 | AC | 2 ms
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testcase_42 | AC | 2 ms
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testcase_43 | AC | 2 ms
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testcase_44 | AC | 2 ms
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testcase_45 | AC | 2 ms
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testcase_46 | AC | 2 ms
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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; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endifnamespace matrix_ {struct has_id_method_impl {template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());template <class T_> static auto check(...) -> std::false_type;};template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};} // namespace matrix_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));}template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2::id();}template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2(1);}static matrix Identity(int N) {matrix ret(N, N);for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();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_id<T>() / 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) != T2()) 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) *= -_T_id<T>(); // To preserve sign of determinant}}ws.clear();for (int w = c; w < W; w++) {if (mtr.at(h, w) != T()) ws.emplace_back(w);}const T hcinv = _T_id<T>() / 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) = T();}c++;}return mtr;}int rank_of_gauss_jordan() const {for (int i = H * W - 1; i >= 0; i--) {if (elem[i] != 0) return i / W + 1;}return 0;}int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }T determinant_of_upper_triangle() const {T ret = _T_id<T>();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_id<T>() / 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); }template <class OStream> friend OStream &operator<<(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;}template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {for (auto &v : x.elem) is >> v;return is;}};// Solve Ax = b for T = ModInt<PRIME>// - retval: {one of the solution, {freedoms}} (if solution exists)// {{}, {}} (otherwise)// Complexity:// - Yield one of the possible solutions: O(HW rank(A)) (H: # of eqs., W: # of variables)// - Enumerate all of the bases: O(W(H + W))template <typename T>std::pair<std::vector<T>, std::vector<std::vector<T>>>system_of_linear_equations(matrix<T> A, std::vector<T> b) {int H = A.height(), W = A.width();matrix<T> M(H, W + 1);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) M[i][j] = A[i][j];M[i][W] = b[i];}M = M.gauss_jordan();std::vector<int> ss(W, -1), ss_nonneg_js;for (int i = 0; i < H; i++) {int j = 0;while (j <= W and M[i][j] == 0) j++;if (j == W) { // No solutionreturn {{}, {}};} else if (j < W) {ss_nonneg_js.push_back(j);ss[j] = i;} else {break;}}std::vector<T> x(W);std::vector<std::vector<T>> D;for (int j = 0; j < W; j++) {if (ss[j] == -1) {// This part may require W^2 space complexity in outputstd::vector<T> d(W);d[j] = 1;for (int jj : ss_nonneg_js) {if (jj >= j) break;d[jj] = -M[ss[jj]][j] / M[ss[jj]][jj];}D.emplace_back(d);} else {x[j] = M[ss[j]][W] / M[ss[j]][j];}}return std::make_pair(x, D);}template <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_;int val() const noexcept { return 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().val() % 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().val() % 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 ModInt inv() const {if (this->val_ < std::min(md >> 1, 1 << 21)) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}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 mint1 = ModInt<998244353>;using mint2 = ModInt<1000000007>;#include <algorithm>#include <cassert>#include <tuple>#include <utility>#include <vector>// CUT begin// Solve ax+by=gcd(a, b)template <class Int> Int extgcd(Int a, Int b, Int &x, Int &y) {Int d = a;if (b != 0) {d = extgcd(b, a % b, y, x), y -= (a / b) * x;} else {x = 1, y = 0;}return d;}// Calculate a^(-1) (MOD m) s if gcd(a, m) == 1// Calculate x s.t. ax == gcd(a, m) MOD mtemplate <class Int> Int mod_inverse(Int a, Int m) {Int x, y;extgcd<Int>(a, m, x, y);x %= m;return x + (x < 0) * m;}// Require: 1 <= b// return: (g, x) s.t. g = gcd(a, b), xa = g MOD b, 0 <= x < b/gtemplate <class Int> /* constexpr */ std::pair<Int, Int> inv_gcd(Int a, Int b) {a %= b;if (a < 0) a += b;if (a == 0) return {b, 0};Int s = b, t = a, m0 = 0, m1 = 1;while (t) {Int u = s / t;s -= t * u, m0 -= m1 * u;auto tmp = s;s = t, t = tmp, tmp = m0, m0 = m1, m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}template <class Int>/* constexpr */ std::pair<Int, Int> crt(const std::vector<Int> &r, const std::vector<Int> &m) {assert(r.size() == m.size());int n = int(r.size());// Contracts: 0 <= r0 < m0Int r0 = 0, m0 = 1;for (int i = 0; i < n; i++) {assert(1 <= m[i]);Int r1 = r[i] % m[i], m1 = m[i];if (r1 < 0) r1 += m1;if (m0 < m1) {std::swap(r0, r1);std::swap(m0, m1);}if (m0 % m1 == 0) {if (r0 % m1 != r1) return {0, 0};continue;}Int g, im;std::tie(g, im) = inv_gcd<Int>(m0, m1);Int u1 = m1 / g;if ((r1 - r0) % g) return {0, 0};Int x = (r1 - r0) / g % u1 * im % u1;r0 += x * m0;m0 *= u1;if (r0 < 0) r0 += m0;}return {r0, m0};}// 蟻本 P.262// 中国剰余定理を利用して,色々な素数で割った余りから元の値を復元// 連立線形合同式 A * x = B mod M の解// Requirement: M[i] > 0// Output: x = first MOD second (if solution exists), (0, 0) (otherwise)template <class Int>std::pair<Int, Int>linear_congruence(const std::vector<Int> &A, const std::vector<Int> &B, const std::vector<Int> &M) {Int r = 0, m = 1;assert(A.size() == M.size());assert(B.size() == M.size());for (int i = 0; i < (int)A.size(); i++) {assert(M[i] > 0);const Int ai = A[i] % M[i];Int a = ai * m, b = B[i] - ai * r, d = std::__gcd(M[i], a);if (b % d != 0) {return std::make_pair(0, 0); // 解なし}Int t = b / d * mod_inverse<Int>(a / d, M[i] / d) % (M[i] / d);r += m * t;m *= M[i] / d;}return std::make_pair((r < 0 ? r + m : r), m);}template <class Int = int, class Long = long long> Int pow_mod(Int x, long long n, Int md) {static_assert(sizeof(Int) * 2 <= sizeof(Long), "Watch out for overflow");if (md == 1) return 0;Int ans = 1;while (n > 0) {if (n & 1) ans = (Long)ans * x % md;x = (Long)x * x % md;n >>= 1;}return ans;}// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {int n = a.size();if (n == 1) return;static const int mod = MODINT::mod();static const MODINT root = MODINT::get_primitive_root();assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);static std::vector<MODINT> w{1}, iw{1};for (int m = w.size(); m < n / 2; m *= 2) {MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;w.resize(m * 2), iw.resize(m * 2);for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;}if (!is_inverse) {for (int m = n; m >>= 1;) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m] * w[k];a[i] = x + y, a[i + m] = x - y;}}}} else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {MODINT x = a[i], y = a[i + m];a[i] = x + y, a[i + m] = (x - y) * iw[k];}}}int n_inv = MODINT(n).inv().val();for (auto &v : a) v *= n_inv;}}template <int MOD>std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);std::vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];ntt(ap, false);if (a == b)bp = ap;elsentt(bp, false);for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long garner_ntt_(int r0, int r1, int r2, int mod) {using mint2 = ModInt<nttprimes[2]>;static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();static const long long m01_inv_m2 = mint2(m01).inv().val();int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;}template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {if (a.empty() or b.empty()) return {};int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {std::vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::mod();if (skip_garner orstd::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {a.resize(sz), b.resize(sz);if (a == b) {ntt(a, false);b = a;} else {ntt(a, false), ntt(b, false);}for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);} else {std::vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val();for (int i = 0; i < m; i++) bi[i] = b[i].val();auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++)a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);}return a;}template <typename MODINT>std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {return nttconv<MODINT>(a, b, false);}template <class mint>vector<mint> solve(int N) {matrix<mint> A(N + 1, N + 1);vector<mint> b(N + 1);b.at(N) = 1;REP(deg, N + 1) {vector<mint> f{mint(deg).facinv()};REP(m, deg) f = nttconv(f, vector<mint>{mint(-m), 1});REP(e, N + 1) {if(e < int(f.size())) A[e][deg] = f.at(e);}}dbg(A);dbg(b);return system_of_linear_equations<mint>(A, b).first;}int main() {int N, M;cin >> N >> M;if (N < M) {puts("0");return 0;}// if (N == 0) {// cout << (M == 0) << endl;// return 0;// }auto sol1 = solve<mint1>(N);auto sol2 = solve<mint2>(N);dbg(sol1);dbg(sol2);cout << linear_congruence<lint>(vector<lint>{1, 1}, vector<lint>{sol1.at(M).val(), sol2.at(M).val()}, vector<lint>{mint1::mod(), mint2::mod()}).first << endl;// exit(1);}