結果
問題 | No.2512 Mountain Sequences |
ユーザー |
|
提出日時 | 2023-10-20 22:18:12 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 43,956 bytes |
コンパイル時間 | 4,423 ms |
コンパイル使用メモリ | 311,096 KB |
最終ジャッジ日時 | 2025-02-17 09:51:51 |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
other | AC * 10 TLE * 1 -- * 18 |
ソースコード
/*** date : 2023-10-20 22:18:03* author : Nyaan*/#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>using minpq = priority_queue<T, vector<T>, greater<T>>;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;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;}template <typename S>P &operator*=(const S &r) {first *= r, second *= r;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; }template <typename S>P operator*(const S &r) const {return P(*this) *= r;}P operator-() const { return P{-first, -second}; }};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;}vector<int> mkiota(int n) {vector<int> ret(n);iota(begin(ret), end(ret), 0);return ret;}template <typename T>T mkrev(const T &v) {T w{v};reverse(begin(w), end(w));return w;}template <typename T>bool nxp(vector<T> &v) {return next_permutation(begin(v), end(v));}// 返り値の型は入力の T に依存// i 要素目 : [0, a[i])template <typename T>vector<vector<T>> product(const vector<T> &a) {vector<vector<T>> ret;vector<T> v;auto dfs = [&](auto rc, int i) -> void {if (i == (int)a.size()) {ret.push_back(v);return;}for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();};dfs(dfs, 0);return ret;}// F : function(void(T&)), mod を取る操作// T : 整数型のときはオーバーフローに注意するtemplate <typename T>T Power(T a, long long n, const T &I, const function<void(T &)> &f) {T res = I;for (; n; f(a = a * a), n >>= 1) {if (n & 1) f(res = res * a);}return res;}// T : 整数型のときはオーバーフローに注意するtemplate <typename T>T Power(T a, long long n, const T &I = T{1}) {return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});}template <typename T>T Rev(const T &v) {T res = v;reverse(begin(res), end(res));return res;}template <typename T>vector<T> Transpose(const vector<T> &v) {using U = typename T::value_type;int H = v.size(), W = v[0].size();vector res(W, T(H, U{}));for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) {res[j][i] = v[i][j];}}return res;}template <typename T>vector<T> Rotate(const vector<T> &v, int clockwise = true) {using U = typename T::value_type;int H = v.size(), W = v[0].size();vector res(W, T(H, U{}));for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) {if (clockwise) {res[W - 1 - j][i] = v[i][j];} else {res[j][H - 1 - i] = v[i][j];}}}return res;}} // 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;}istream &operator>>(istream &is, __int128_t &x) {string S;is >> S;x = 0;int flag = 0;for (auto &c : S) {if (c == '-') {flag = true;continue;}x *= 10;x += c - '0';}if (flag) x = -x;return is;}istream &operator>>(istream &is, __uint128_t &x) {string S;is >> S;x = 0;for (auto &c : S) {x *= 10;x += c - '0';}return is;}ostream &operator<<(ostream &os, __int128_t x) {if (x == 0) return os << 0;if (x < 0) os << '-', x = -x;string S;while (x) S.push_back('0' + x % 10), x /= 10;reverse(begin(S), end(S));return os << S;}ostream &operator<<(ostream &os, __uint128_t x) {if (x == 0) return os << 0;string S;while (x) S.push_back('0' + x % 10), x /= 10;reverse(begin(S), end(S));return os << S;}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...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debug#ifdef NyaanDebug#define trc(...) (void(0))#else#define trc(...) (void(0))#endif#ifdef NyaanLocal#define trc2(...) (void(0))#else#define trc2(...) (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(); }//using namespace std;// {rank, det(非正方行列の場合は未定義)} を返す// 型が double や Rational でも動くはず?(未検証)//// pivot 候補 : [0, pivot_end)template <typename T>std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1,bool diagonalize = false) {int H = a.size(), W = a[0].size(), rank = 0;if (pivot_end == -1) pivot_end = W;T det = 1;for (int j = 0; j < pivot_end; j++) {int idx = -1;for (int i = rank; i < H; i++) {if (a[i][j] != T(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] != T(1)) {T coeff = T(1) / a[rank][j];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] != T(0)) {T 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);}// 解が存在する場合は, 解が v + C_1 w_1 + ... + C_k w_k と表せるとして// (v, w_1, ..., w_k) を返す// 解が存在しない場合は空のベクトルを返す//// double や Rational でも動くはず?(未検証)template <typename T>vector<vector<T>> LinearEquation(vector<vector<T>> a, vector<T> b) {int H = a.size(), W = a[0].size();for (int i = 0; i < H; i++) a[i].push_back(b[i]);auto p = GaussElimination(a, W, true);int rank = p.first;for (int i = rank; i < H; ++i) {if (a[i][W] != 0) return vector<vector<T>>{};}vector<vector<T>> res(1, vector<T>(W));vector<int> pivot(W, -1);for (int i = 0, j = 0; i < rank; ++i) {while (a[i][j] == 0) ++j;res[0][j] = a[i][W], pivot[j] = i;}for (int j = 0; j < W; ++j) {if (pivot[j] == -1) {vector<T> x(W);x[j] = 1;for (int k = 0; k < j; ++k) {if (pivot[k] != -1) x[k] = -a[pivot[k]][j];}res.push_back(x);}}return res;}template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inverse();for (auto &x : g) x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0)) this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];return ret;}// 前 sz 項を取ってくる。sz に足りない項は 0 埋めするFPS pre(int sz) const {FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));if ((int)ret.size() < sz) ret.resize(sz);return ret;}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::get_mod();for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this) r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert(!(*this).empty() && (*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void *ntt_ptr;static void set_fft();FPS &operator*=(const FPS &r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void *FormalPowerSeries<mint>::ntt_ptr = nullptr;/*** @brief 多項式/形式的冪級数ライブラリ* @docs docs/fps/formal-power-series.md*/using namespace std;// コンストラクタの MAX に 「C(n, r) や fac(n) でクエリを投げる最大の n 」// を入れると倍速くらいになる// mod を超えて前計算して 0 割りを踏むバグは対策済みtemplate <typename T>struct Binomial {vector<T> f, g, h;Binomial(int MAX = 0) {assert(T::get_mod() != 0 && "Binomial<mint>()");f.resize(1, T{1});g.resize(1, T{1});h.resize(1, T{1});if (MAX > 0) extend(MAX + 1);}void extend(int m = -1) {int n = f.size();if (m == -1) m = n * 2;m = min<int>(m, T::get_mod());if (n >= m) return;f.resize(m);g.resize(m);h.resize(m);for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);g[m - 1] = f[m - 1].inverse();h[m - 1] = g[m - 1] * f[m - 2];for (int i = m - 2; i >= n; i--) {g[i] = g[i + 1] * T(i + 1);h[i] = g[i] * f[i - 1];}}T fac(int i) {if (i < 0) return T(0);while (i >= (int)f.size()) extend();return f[i];}T finv(int i) {if (i < 0) return T(0);while (i >= (int)g.size()) extend();return g[i];}T inv(int i) {if (i < 0) return -inv(-i);while (i >= (int)h.size()) extend();return h[i];}T C(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r) * finv(r);}inline T operator()(int n, int r) { return C(n, r); }template <typename I>T multinomial(const vector<I>& r) {static_assert(is_integral<I>::value == true);int n = 0;for (auto& x : r) {if (x < 0) return T(0);n += x;}T res = fac(n);for (auto& x : r) res *= finv(x);return res;}template <typename I>T operator()(const vector<I>& r) {return multinomial(r);}T C_naive(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);T ret = T(1);r = min(r, n - r);for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);return ret;}T P(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r);}// [x^r] 1 / (1-x)^nT H(int n, int r) {if (n < 0 || r < 0) return T(0);return r == 0 ? 1 : C(n + r - 1, r);}};// input : y(0), y(1), ..., y(n - 1)// output : y(t), y(t + 1), ..., y(t + m - 1)// (if m is default, m = n)template <typename mint>FormalPowerSeries<mint> SamplePointShift(FormalPowerSeries<mint>& y, mint t,int m = -1) {if (m == -1) m = y.size();long long T = t.get();int k = (int)y.size() - 1;T %= mint::get_mod();if (T <= k) {FormalPowerSeries<mint> ret(m);int ptr = 0;for (int64_t i = T; i <= k and ptr < m; i++) {ret[ptr++] = y[i];}if (k + 1 < T + m) {auto suf = SamplePointShift<mint>(y, k + 1, m - ptr);for (int i = k + 1; i < T + m; i++) {ret[ptr++] = suf[i - (k + 1)];}}return ret;}if (T + m > mint::get_mod()) {auto pref = SamplePointShift<mint>(y, T, mint::get_mod() - T);auto suf = SamplePointShift<mint>(y, 0, m - pref.size());copy(begin(suf), end(suf), back_inserter(pref));return pref;}FormalPowerSeries<mint> finv(k + 1, 1), d(k + 1);for (int i = 2; i <= k; i++) finv[k] *= i;finv[k] = mint(1) / finv[k];for (int i = k; i >= 1; i--) finv[i - 1] = finv[i] * i;for (int i = 0; i <= k; i++) {d[i] = finv[i] * finv[k - i] * y[i];if ((k - i) & 1) d[i] = -d[i];}FormalPowerSeries<mint> h(m + k);for (int i = 0; i < m + k; i++) {h[i] = mint(1) / (T - k + i);}auto dh = d * h;FormalPowerSeries<mint> ret(m);mint cur = T;for (int i = 1; i <= k; i++) cur *= T - i;for (int i = 0; i < m; i++) {ret[i] = cur * dh[k + i];cur *= T + i + 1;cur *= h[i];}return ret;}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;}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;}Matrix inverse() const {assert(H() == W());Matrix B(H());B.A = inverse_matrix(A);return B;}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*/// return m(k-1) * m(k-2) * ... * m(1) * m(0)template <typename mint>Matrix<mint> polynomial_matrix_prod(Matrix<FormalPowerSeries<mint>> &m,long long k) {using Mat = Matrix<mint>;using fps = FormalPowerSeries<mint>;auto shift = [](vector<Mat> &G, mint x) -> vector<Mat> {int d = G.size(), n = G[0].size();vector<Mat> H(d, Mat(n));for (int i = 0; i < n; i++) {for (int j = 0; j < n; j++) {fps g(d);for (int l = 0; l < d; l++) g[l] = G[l][i][j];fps h = SamplePointShift(g, x);for (int l = 0; l < d; l++) H[l][i][j] = h[l];}}return H;};int n = m.size();int deg = 1;for (auto &_ : m.A) {for (auto &x : _) deg = max<int>(deg, (int)x.size() - 1);}while (deg & (deg - 1)) deg++;vector<Mat> G(deg + 1);long long v = 1;while (deg * v * v < k) v *= 2;mint iv = mint(v).inverse();for (int i = 0; i < (int)G.size(); i++) {mint x = mint(v) * i;Mat mt(n);for (int j = 0; j < n; j++)for (int l = 0; l < n; l++) mt[j][l] = m[j][l].eval(x);G[i] = mt;}for (long long w = 1; w != v; w <<= 1) {mint W = w;auto G1 = shift(G, W * iv);auto G2 = shift(G, (W * deg * v + v) * iv);auto G3 = shift(G, (W * deg * v + v + W) * iv);for (int i = 0; i <= w * deg; i++)G[i] = G1[i] * G[i], G2[i] = G3[i] * G2[i];copy(begin(G2), end(G2) - 1, back_inserter(G));}Mat res = Mat::I(n);long long i = 0;while (i + v <= k) res = G[i / v] * res, i += v;while (i < k) {Mat mt(n);for (int j = 0; j < n; j++)for (int l = 0; l < n; l++) mt[j][l] = m[j][l].eval(i);res = mt * res;i++;}return res;}/*** @brief 多項式行列のprefix product*/// return polynomial coefficient s.t. sum_{j=k...0} f_j(i) a_{i+j} = 0// (In more details, read verification code.)template <typename mint>vector<FormalPowerSeries<mint>> find_p_recursive(vector<mint>& a, int d) {using fps = FormalPowerSeries<mint>;int n = a.size();int k = (n + 2) / (d + 2) - 1;if (k <= 0) return {};int m = (k + 1) * (d + 1);vector<vector<mint>> M(m - 1, vector<mint>(m));for (int i = 0; i < m - 1; i++) {for (int j = 0; j <= k; j++) {mint base = 1;for (int l = 0; l <= d; l++) {M[i][(d + 1) * j + l] = base * a[i + j];base *= i + j;}}}auto gauss = LinearEquation<mint>(M, vector<mint>(m - 1, 0));if (gauss.size() <= 1) return {};auto c = gauss[1];while (all_of(end(c) - d - 1, end(c), [](mint x) { return x == mint(0); })) {c.erase(end(c) - d - 1, end(c));}k = c.size() / (d + 1) - 1;vector<fps> res;for (int i = 0, j = 0; i < (int)c.size(); i += d + 1, j++) {fps f{1}, base{j, 1};fps sm;for (int l = 0; l <= d; l++) sm += f * c[i + l], f *= base;res.push_back(sm);}reverse(begin(res), end(res));return res;}template <typename mint>mint kth_term_of_p_recursive(vector<mint>& a, long long k, int d) {if (k < (int)a.size()) return a[k];if (all_of(begin(a), end(a), [](mint x) { return x == mint(0); })) return 0;auto fs = find_p_recursive(a, d);assert(fs.empty() == false);int deg = fs.size() - 1;assert(deg >= 1);Matrix<FormalPowerSeries<mint>> m(deg), denom(1);for (int i = 0; i < deg; i++) m[0][i] = -fs[i + 1];for (int i = 1; i < deg; i++) m[i][i - 1] = fs[0];denom[0][0] = fs[0];Matrix<mint> a0(deg);for (int i = 0; i < deg; i++) a0[i][0] = a[deg - 1 - i];mint res = (polynomial_matrix_prod(m, k - deg + 1) * a0)[0][0];res /= polynomial_matrix_prod(denom, k - deg + 1)[0][0];return res;}template <typename mint>mint kth_term_of_p_recursive(vector<mint>& a, long long k) {if (k < (int)a.size()) return a[k];if (all_of(begin(a), end(a), [](mint x) { return x == mint(0); })) return 0;int n = a.size() - 1;vector<mint> b{begin(a), end(a) - 1};for (int d = 0;; d++) {#ifdef NyaanLocalcerr << "d = " << d << endl;#endifif ((n + 2) / (d + 2) <= 1) break;if (kth_term_of_p_recursive(b, n, d) == a.back()) {#ifdef NyaanLocalcerr << "Found, d = " << d << endl;#endifreturn kth_term_of_p_recursive(a, k, d);}}cerr << "Failed." << endl;exit(1);}/*** @brief P-recursiveの高速計算* @docs docs/fps/find-p-recursive.md*///template <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0) m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, __builtin_ctz(a.size()));}void intt(vector<mint> &a) {if ((int)a.size() <= 1) return;ifft4(a, __builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for (auto &x : a) x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l) M <<= 1, ++k;setwy(k);vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i) s[i] *= s[i];} else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i) s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inverse();for (int i = 0; i < l; ++i) s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint>*>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> res(deg);res[0] = {mint(1) / (*this)[0]};for (int d = 1; d < deg; d <<= 1) {FormalPowerSeries<mint> f(2 * d), g(2 * d);for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];for (int j = 0; j < d; j++) g[j] = res[j];f.ntt();g.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = 0; j < d; j++) f[j] = 0;f.ntt();for (int j = 0; j < 2 * d; j++) f[j] *= g[j];f.intt();for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];}return res.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {using fps = FormalPowerSeries<mint>;assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = this->size();fps inv;inv.reserve(deg + 1);inv.push_back(mint(0));inv.push_back(mint(1));auto inplace_integral = [&](fps& F) -> void {const int n = (int)F.size();auto mod = mint::get_mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), mint(0));for (int i = 1; i <= n; i++) F[i] *= inv[i];};auto inplace_diff = [](fps& F) -> void {if (F.empty()) return;F.erase(begin(F));mint coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);y.ntt();z1 = z2;fps z(m);for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];z.intt();fill(begin(z), begin(z) + m / 2, mint(0));z.ntt();for (int i = 0; i < m; ++i) z[i] *= -z1[i];z.intt();c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);z2.ntt();fps x(begin(*this), begin(*this) + min<int>(this->size(), m));x.resize(m);inplace_diff(x);x.push_back(mint(0));x.ntt();for (int i = 0; i < m; ++i) x[i] *= y[i];x.intt();x -= b.diff();x.resize(2 * m);for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];x.intt();x.pop_back();inplace_integral(x);for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];fill(begin(x), begin(x) + m, mint(0));x.ntt();for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];x.intt();b.insert(end(b), begin(x) + m, end(x));}return fps{begin(b), begin(b) + deg};}/*** @brief NTT mod用FPSライブラリ* @docs docs/fps/ntt-friendly-fps.md*/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(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");static_assert(r * mod == 1, "this code has bugs.");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 operator+() const { return 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 {int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;while (y > 0) {t = x / y;x -= t * y, u -= t * v;tmp = x, x = y, y = tmp;tmp = u, u = v, v = tmp;}return mint{u};}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; }};// #include "fps/arbitrary-fps.hpp"//using namespace Nyaan;using mint = LazyMontgomeryModInt<998244353>;// using mint = LazyMontgomeryModInt<1000000007>;using vm = vector<mint>;using vvm = vector<vm>;Binomial<mint> C;using fps = FormalPowerSeries<mint>;using namespace Nyaan;mint naive(ll N, ll M) {mint ans = 0;rep1(x, M) { ans += C(2 * x - 2, N - 1); }return ans;}mint calc(ll N, ll M) {// C(0,N-1), C(2, N-1), ..., C(2M-2, N-1)int lower = (N - 1 + 1) / 2;if(lower>=M)return 0;/*mint ans = 0;reg(i, lower, M) ans += C(i * 2, N - 1);return ans;*/vm a;mint ans = 0;reg(i, lower, lower + 20) ans += C(i * 2, N - 1), a.push_back(ans);return kth_term_of_p_recursive(a, M - lower - 1);}void q() {/*rep(i, 100) rep(j, 100) {trc(i, j, naive(i, j), calc(i, j));assert(naive(i, j) == calc(i, j));}*/inl(T);while (T--) {inl(N, M);out(calc(N, M));}}void Nyaan::solve() {int t = 1;// in(t);while (t--) q();}