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#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3361" #include <cassert> #include <iostream> #include <vector> #include "../../fps/fps_sparse.hpp" #include "../../math/binomial.hpp" #include "../../modint/modint.hpp" using mint = ebi::modint998244353; int main() { int k, n; std::vector<mint> f(300); ebi::Binomial<mint> comb(1000000); f[1] = 1; f[256] = -256; f[257] = 255; while (std::cin >> k >> n, !(n == 0 && k == 0)) { auto dp = ebi::pow_sparse(f, k, n + 1); assert(int(dp.size()) == n + 1); mint ans = 0; for (int i = n; i >= 0; i--) { ans += dp[i] * comb.c(2 * k - 1 + n - i, n - i); } std::cout << ans.val() << '\n'; } }
#line 1 "test/aoj/aoj_3361.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3361" #include <cassert> #include <iostream> #include <vector> #line 2 "fps/fps_sparse.hpp" #line 5 "fps/fps_sparse.hpp" #line 2 "math/mod_inv.hpp" #line 5 "math/mod_inv.hpp" #line 2 "modint/base.hpp" #include <concepts> #line 5 "modint/base.hpp" #include <utility> namespace ebi { template <class T> concept Modint = requires(T a, T b) { a + b; a - b; a * b; a / b; a.inv(); a.val(); a.pow(std::declval<long long>()); T::mod(); }; template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) { long long x; os >> x; a = x; return os; } template <Modint mint> std::ostream &operator<<(std::ostream &os, const mint &a) { return os << a.val(); } } // namespace ebi #line 7 "math/mod_inv.hpp" namespace ebi { template <Modint mint> mint inv(int n) { static const int mod = mint::mod(); static std::vector<mint> dat = {0, 1}; assert(0 <= n); if (n >= mod) n -= mod; while (int(dat.size()) <= n) { int num = dat.size(); int q = (mod + num - 1) / num; dat.emplace_back(dat[num * q - mod] * mint(q)); } return dat[n]; } } // namespace ebi #line 8 "fps/fps_sparse.hpp" namespace ebi { template <Modint mint> std::vector<mint> mul_sparse(const std::vector<mint> &f, const std::vector<mint> &g) { int n = f.size(); int m = g.size(); std::vector<std::pair<int, mint>> cf, cg; for (int i = 0; i < n; i++) { if (f[i] != 0) cf.emplace_back(i, f[i]); } for (int i = 0; i < m; i++) { if (g[i] != 0) cg.emplace_back(i, g[i]); } std::vector<mint> h(n + m - 1); for (auto [i, p] : cf) { for (auto [j, q] : cg) { h[i + j] += p * q; } } return h; } template <Modint mint> std::vector<mint> inv_sparse(const std::vector<mint> &f, int d = -1) { assert(f[0] != 0); if (d < 0) { d = f.size(); } std::vector<std::pair<int, mint>> ret; for (int i = 1; i < int(f.size()); i++) { if (f[i] != 0) { ret.emplace_back(i, f[i]); } } std::vector<mint> g(d); g[0] = f[0].inv(); for (int i = 1; i < d; i++) { for (auto [k, p] : ret) { if (i - k < 0) break; g[i] -= g[i - k] * p; } g[i] *= g[0]; } return g; } template <Modint mint> std::vector<mint> exp_sparse(const std::vector<mint> &f, int d = -1) { int n = f.size(); if (d < 0) d = n; std::vector<std::pair<int, mint>> ret; for (int i = 1; i < n; i++) { if (f[i] != 0) { ret.emplace_back(i - 1, f[i] * i); } } std::vector<mint> g(d); g[0] = 1; for (int i = 0; i < d - 1; i++) { for (auto [k, p] : ret) { if (i - k < 0) break; g[i + 1] += g[i - k] * p; } g[i + 1] *= inv<mint>(i + 1); } return g; } template <Modint mint> std::vector<mint> log_sparse(const std::vector<mint> &f, int d = -1) { int n = f.size(); if (d < 0) d = n; std::vector<mint> df(d); for (int i = 0; i < std::min(d, n - 1); i++) { df[i] = f[i + 1] * (i + 1); } auto dg = mul_sparse(df, inv_sparse(f)); dg.resize(d); std::vector<mint> g(d); for (int i = 0; i < d - 1; i++) { g[i + 1] = dg[i] * inv<mint>(i + 1); } return g; } template <Modint mint> std::vector<mint> pow_sparse_1(const std::vector<mint> &f, long long k, int d = -1) { int n = f.size(); assert(n == 0 || f[0] == 1); std::vector<std::pair<int, mint>> ret; for (int i = 1; i < n; i++) { if (f[i] != 0) ret.emplace_back(i, f[i]); } std::vector<mint> g(d); g[0] = 1; for (int i = 0; i < d - 1; i++) { for (const auto &[j, cf] : ret) { if (i + 1 - j < 0) break; g[i + 1] += (mint(k) * mint(j) - mint(i - j + 1)) * cf * g[i + 1 - j]; } g[i + 1] *= inv<mint>(i + 1); } return g; } template <Modint mint> std::vector<mint> pow_sparse(const std::vector<mint> &f, long long k, int d = -1) { int n = f.size(); if (d < 0) d = n; assert(k >= 0); if (k == 0) { std::vector<mint> g(d); if (d > 0) g[0] = 1; return g; } for (int i = 0; i < n; i++) { if (f[i] != 0) { mint rev = f[i].inv(); std::vector<mint> f2(n - i); for (int j = i; j < n; j++) { f2[j - i] = f[j] * rev; } f2 = pow_sparse_1(f2, k, d); mint fk = f[i].pow(k); std::vector<mint> g(d); for (int j = 0; j < int(f2.size()); j++) { if (j + i * k >= d) break; g[j + i * k] = f2[j] * fk; } return g; } if (i >= (d + k - 1) / k) break; } return std::vector<mint>(d); } } // namespace ebi #line 2 "math/binomial.hpp" #include <bit> #line 6 "math/binomial.hpp" #include <ranges> #line 8 "math/binomial.hpp" #line 10 "math/binomial.hpp" namespace ebi { template <Modint mint> struct Binomial { private: static void extend(int len = -1) { int sz = (int)fact.size(); if (len < 0) len = 2 * sz; else if (len <= sz) return; else len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len))); len = std::min(len, mint::mod()); assert(sz <= len); fact.resize(len); inv_fact.resize(len); for (int i : std::views::iota(sz, len)) { fact[i] = fact[i - 1] * i; } inv_fact[len - 1] = fact[len - 1].inv(); for (int i : std::views::iota(sz, len) | std::views::reverse) { inv_fact[i - 1] = inv_fact[i] * i; } } public: Binomial() = default; Binomial(int n) { extend(n + 1); } static mint f(int n) { if (n >= (int)fact.size()) [[unlikely]] { extend(n + 1); } return fact[n]; } static mint inv_f(int n) { if (n >= (int)fact.size()) [[unlikely]] { extend(n + 1); } return inv_fact[n]; } static mint c(int n, int r) { if (r < 0 || n < r) return 0; return f(n) * inv_f(r) * inv_f(n - r); } static mint p(int n, int r) { if (r < 0 || n < r) return 0; return f(n) * inv_f(n - r); } static mint inv(int n) { return inv_f(n) * f(n - 1); } static void reserve(int n) { extend(n + 1); } private: static std::vector<mint> fact, inv_fact; }; template <Modint mint> std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1); template <Modint mint> std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1); } // namespace ebi #line 2 "modint/modint.hpp" #line 5 "modint/modint.hpp" #line 7 "modint/modint.hpp" namespace ebi { template <int m> struct static_modint { private: using modint = static_modint; public: static constexpr int mod() { return m; } static constexpr modint raw(int v) { modint x; x._v = v; return x; } constexpr static_modint() : _v(0) {} constexpr static_modint(long long v) { v %= (long long)umod(); if (v < 0) v += (long long)umod(); _v = (unsigned int)v; } constexpr unsigned int val() const { return _v; } constexpr unsigned int value() const { return val(); } constexpr modint &operator++() { _v++; if (_v == umod()) _v = 0; return *this; } constexpr modint &operator--() { if (_v == 0) _v = umod(); _v--; return *this; } constexpr modint operator++(int) { modint res = *this; ++*this; return res; } constexpr modint operator--(int) { modint res = *this; --*this; return res; } constexpr modint &operator+=(const modint &rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } constexpr modint &operator-=(const modint &rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } constexpr modint &operator*=(const modint &rhs) { unsigned long long x = _v; x *= rhs._v; _v = (unsigned int)(x % (unsigned long long)umod()); return *this; } constexpr modint &operator/=(const modint &rhs) { return *this = *this * rhs.inv(); } constexpr modint operator+() const { return *this; } constexpr modint operator-() const { return modint() - *this; } constexpr modint pow(long long n) const { assert(0 <= n); modint x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } constexpr modint inv() const { assert(_v); return pow(umod() - 2); } friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += rhs; } friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= rhs; } friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= rhs; } friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= rhs; } friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.val() == rhs.val(); } friend bool operator!=(const modint &lhs, const modint &rhs) { return !(lhs == rhs); } private: unsigned int _v = 0; static constexpr unsigned int umod() { return m; } }; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; } // namespace ebi #line 10 "test/aoj/aoj_3361.test.cpp" using mint = ebi::modint998244353; int main() { int k, n; std::vector<mint> f(300); ebi::Binomial<mint> comb(1000000); f[1] = 1; f[256] = -256; f[257] = 255; while (std::cin >> k >> n, !(n == 0 && k == 0)) { auto dp = ebi::pow_sparse(f, k, n + 1); assert(int(dp.size()) == n + 1); mint ans = 0; for (int i = n; i >= 0; i--) { ans += dp[i] * comb.c(2 * k - 1 + n - i, n - i); } std::cout << ans.val() << '\n'; } }