#if ! defined(ONLINE_JUDGE) && __has_include("template.hpp") #include "template.hpp" #else // template start #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using pall = pair; template using vec = vector; template using veve = vec>; using vell = vec; using vest = vec; using vepl = vec; using vebo = basic_string; using vevell = veve; using vevepl = veve; template using mset = multiset; template using priority_queue_ascend = priority_queue, greater>; constexpr ll inf = numeric_limits::max() / 4; constexpr string sp{" "}; constexpr string lf{"\n"}; constexpr auto npos = string::npos; constexpr array grid_move4{{{0, 1}, {-1, 0}, {0, -1}, {1, 0}}}; constexpr array grid_move8{ {{0, 1}, {-1, 0}, {0, -1}, {1, 0}, {-1, 1}, {-1, -1}, {1, -1}, {1, 1}}}; template constexpr auto minf = [](T x, T y) { return min(x, y); }; template constexpr auto maxf = [](T x, T y) { return max(x, y); }; #define cont continue #define ocnt cont #define br break #define whlie while #define whiel while #define foR for #define reutnr return #define retunr return #define reutrn return #define auot auto #define uato auto #define uaot auto #define atuo auto #define cosnt const #define conts const #define ocnst const #define isze size inline auto &ciN = cin; inline auto &icn = cin; inline auto &icN = cin; constexpr bool ture = true; constexpr bool tuer = true; constexpr bool flase = false; namespace ra = std::ranges; namespace vi = views; using namespace atcoder; #define times(N) \ static_assert(is_integral_v>, "times(): N must be integral"); \ if(const auto &_N = (N); _N >= 0) \ for(typedef remove_cvref_t _int; \ [[maybe_unused]] const _int ii : views::iota((_int)0, _N)) #define tiems times #define itmes times #define lmd(e) \ [&]([[maybe_unused]] T1 &&_1 = {}, \ [[maybe_unused]] T2 &&_2 = {}, \ [[maybe_unused]] T3 &&_3 = {}, \ [[maybe_unused]] T4 &&_4 = {}, \ [[maybe_unused]] T5 &&_5 = {}, \ [[maybe_unused]] T6 &&_6 = {}, \ [[maybe_unused]] T7 &&_7 = {}, \ [[maybe_unused]] T8 &&_8 = {}, \ [[maybe_unused]] T9 &&_9 = {}) -> decltype(auto) { return e; } #define lmd_aply(e) \ [&](T &&t) -> decltype(auto) { return apply(lmd(e), std::forward(t)); } struct no_output_stream { no_output_stream &operator<<(auto &&) { return *this; } no_output_stream &operator<<(std::ostream &(*)(std::ostream &)) { return *this; } no_output_stream &operator<<(std::ios_base &(*)(std::ios_base &)) { return *this; } }; #ifdef ONLINE_JUDGE inline no_output_stream clog_; #define clog clog_ #endif template concept out_stream = same_as || same_as; template istream &operator>>(istream &in, static_modint &i) { ll tmp; in >> tmp; i = tmp; return in; } template istream &operator>>(istream &in, dynamic_modint &i) { ll tmp; in >> tmp; i = tmp; return in; } template out_stream auto &operator<<(out_stream auto &out, const static_modint &i) { return out << i.val(); } template out_stream auto &operator<<(out_stream auto &out, const dynamic_modint &i) { return out << i.val(); } template istream &operator>>(istream &in, pair &p) { return in >> p.first >> p.second; } template out_stream auto &operator<<(out_stream auto &out, const pair &p) { return out << p.first << sp << p.second; } template istream &operator>>(istream &in, vec &v) { for(auto &e : v) { in >> e; } return in; } template istream &in(Ts &...vecs) { static_assert(sizeof...(vecs) != 0, "myfunc::in(): At least one vector must be provided"); const array sizes = {vecs.size()...}; if(ra::find_if(sizes, lmd(_1 != sizes[0])) != sizes.end()) { throw invalid_argument("myfunc::in(): All vectors must have the same size"); } times(*sizes.begin()) { ((cin >> vecs[ii]), ...); } return cin; } auto out(std::ranges::input_range auto &&v, const string &delim, out_stream auto &out) -> add_lvalue_reference_t { for(auto &&e : v) { out << e << delim; } return out; } decltype(auto) out(std::ranges::input_range auto &&v, const string &delim) { return out(v, delim, cout); } inline void yes() { cout << "Yes" << lf; } inline void no() { cout << "No" << lf; } inline void yesu() { cout << "YES" << lf; } inline void nou() { cout << "NO" << lf; } // [mi, ma) [[nodiscard]] inline uint64_t randint(const uint64_t mi, const uint64_t ma) { static mt19937_64 mt(random_device{}()); assert(mi != ma); if(mi > ma) [[unlikely]] return randint(ma, mi); const uint64_t w = ma - mi; uint64_t r; do { r = mt(); } while(mt.max() - mt.max() % w <= r); return r % w + mi; } template requires common_with && (not is_reference_v>) [[nodiscard]] constexpr auto min(T &&a, U &&b) { using CT = common_type_t; static_assert( requires (CT ca, CT cb) { { ca < cb } -> convertible_to; }, "common type must be comparable"); if constexpr(requires () { { b < a } -> convertible_to; }) { if(b < a) return CT(std::forward(b)); else return CT(std::forward(a)); } else { const CT ca(std::forward(a)); const CT cb(std::forward(b)); return (cb < ca) ? cb : ca; } } template [[nodiscard]] constexpr const T &min(T &a, T &b) { return std::min(a, b); } template requires common_with && (not is_reference_v>) [[nodiscard]] constexpr auto max(T &&a, U &&b) { using CT = common_type_t; static_assert( requires (CT ca, CT cb) { { ca < cb } -> convertible_to; }, "common type must be comparable"); if constexpr(requires () { { a < b } -> convertible_to; }) { if(a < b) return CT(std::forward(b)); else return CT(std::forward(a)); } else { const CT ca(std::forward(a)); const CT cb(std::forward(b)); return (ca < cb) ? cb : ca; } } template [[nodiscard]] constexpr const T &max(T &a, T &b) { return std::max(a, b); } template [[nodiscard]] auto reduce(std::ranges::input_range auto &&r, Args &&...args) { auto &&cr = views::common(std::forward(r)); return std::reduce(std::ranges::begin(cr), std::ranges::end(cr), std::forward(args)...); } template auto popcount(T x) { return popcount(static_cast>(x)); } template auto bit_width(T x) { return bit_width(static_cast>(x)); } template auto bit_floor(T x) { return bit_floor(static_cast>(x)); } template auto bit_ceil(T x) { return bit_ceil(static_cast>(x)); } [[nodiscard]] constexpr ll powll(ll a, ll b, const ll m = numeric_limits::max()) { if(b < 0) [[unlikely]] throw invalid_argument("powll(): exponent less than zero"); if(m < 1) [[unlikely]] throw invalid_argument("powll(): modulo less than one"); a %= m; ll ret = 1; while(b) { if(b % 2) ret *= a, ret %= m; a *= a, a %= m; b /= 2; } return ret; } template requires assignable_from && totally_ordered_with bool mini(T &var, U &&val) { const bool cmp = var > val; if(cmp) var = std::forward(val); return cmp; } template requires assignable_from && totally_ordered_with bool maxi(T &var, U &&val) { const bool cmp = var < val; if(cmp) var = std::forward(val); return cmp; } template class Map, class K, class V> requires same_as, map> || same_as, unordered_map> [[nodiscard]] const V &vmin(const Map &m) { assert(not m.empty()); return *std::ranges::min_element(m | views::values); } template class Map, class K, class V> requires same_as, map> || same_as, unordered_map> [[nodiscard]] const V &vmax(const Map &m) { assert(not m.empty()); return *std::ranges::max_element(m | views::values); } class [[nodiscard]] grid { public: grid(const ll h, const ll w) noexcept : height(h), width(w) {} [[nodiscard]] ll operator()(const ll i, const ll j) const noexcept { if(not isvalid(i, j)) return -1; return i * width + j; } [[nodiscard]] ll operator()(const pall &p) const noexcept { return (*this)(p.first, p.second); } protected: bool isvalid(const ll i, const ll j) const noexcept { return 0 <= i && 0 <= j && i < height && j < width; } const ll height, width; }; class [[nodiscard]] grid_seen : public grid { public: grid_seen(const ll h, const ll w) : grid(h, w) { visited = vebo(h * w, false); } [[nodiscard]] bool &seen(const ll i, const ll j) & { if(not isvalid(i, j)) [[unlikely]] throw out_of_range("grid_seen::seen(): out of range"); return visited[i * width + j]; } [[nodiscard]] bool &seen(const pall &p) & { return seen(p.first, p.second); } template [[nodiscard]] bool &sen(Args &&...args) & { return seen(forward(args)...); } private: vebo visited; }; template requires convertible_to::mapped_type> class default_map : public map { using Map = map; template static constexpr bool comparable = requires (Map::key_compare c, Map::key_type t, U u) { c(t, u); c(u, t); }; public: #ifdef __cpp_lib_associative_heterogeneous_insertion template U> requires comparable Map::mapped_type &operator[](const U &key) { Map::try_emplace(key, defval); return Map::operator[](key); } template U> requires comparable Map::mapped_type &operator[](const U &&key) { Map::try_emplace(key, defval); return Map::operator[](key); } #else Map::mapped_type &operator[](const Map::key_type &key) { Map::try_emplace(key, defval); return Map::operator[](key); } Map::mapped_type &operator[](const Map::key_type &&key) { Map::try_emplace(key, defval); return Map::operator[](key); } #endif }; template requires is_convertible_v::mapped_type> class default_unordered_map : public unordered_map { using Map = unordered_map; template static constexpr bool hashable = requires (Map::hasher h, U u) { h(u); }; public: #ifdef __cpp_lib_associative_heterogeneous_insertion template requires hashable Map::mapped_type &operator[](const U &key) { Map::try_emplace(key, defval); return Map::operator[](key); } template requires hashable Map::mapped_type &operator[](const U &&key) { Map::try_emplace(key, defval); return Map::operator[](key); } #else Map::mapped_type &operator[](const Map::key_type &key) { Map::try_emplace(key, defval); return Map::operator[](key); } Map::mapped_type &operator[](const Map::key_type &&key) { Map::try_emplace(key, defval); return Map::operator[](key); } #endif }; template requires requires (mset::key_compare c, T t, U u) { { c(t, u) } -> convertible_to; } auto erase_single(mset &mset, U &&v) { const auto it = mset.find(v); if(it == mset.end()) return mset.end(); return mset.erase(it); } inline ll isqrt(const ll x) { assert(x >= 0); ll rx = (ll)sqrt(x); while((rx + 1) * (rx + 1) <= x) rx++; while(rx * rx > x) rx--; return rx; } inline ll divceil(const ll a, const ll b) { assert(b != 0); return (a + b - 1) / b; } // template end #endif #define MOD_IS_998 1 #ifdef MOD_IS_998 using mint = modint998244353; #else using mint = modint1000000007; #endif constexpr ll MOD = mint::mod(); static void init(); static void solve(); int main(void) { cin.tie(nullptr); ios::sync_with_stdio(false); init(); ll t = 1; // cin >> t; times(t) solve(); return 0; } void init() {} #include #include #include #include #include using namespace std; using ll = long long; template using mat = array, H>; template auto mul(const mat &a, const mat &b) { static_assert(W1 == H2, "W1 must be equal to H2"); mat res{}; for(size_t i = 0; i < H1; i++) { for(size_t j = 0; j < W2; j++) { for(size_t k = 0; k < W1; k++) { res[i][j] += a[i][k] * b[k][j]; } } } return res; } template auto pow(mat a, ll e) { if(e < 0) [[unlikely]] throw invalid_argument("pow(): exponent less than zero"); mat ret{}; for(size_t i = 0; i < N; i++) { ret[i][i] = 1; } while(e) { if(e % 2) ret = mul(ret, a); a = mul(a, a); e /= 2; } return ret; } void solve() { ll n, k; cin >> n >> k; // dp[i + 1] = (1 / 5) * dp[i]; // dp[0] = (4 / 5) * sum(dp[:4n]) mat dp; for(intmax_t i = 0; i <= intmax_t(4 * n); i++) { for(intmax_t j = 0; j <= intmax_t(4 * n); j++) { dp[i][j] = 0; } } for(intmax_t i = 0; i < intmax_t(4 * n); i++) { dp[i][i + 1] = mint(1) / 5; if(i % 4 == 0) { dp[i][0] = mint(4) / 5; } else { dp[i][0] = mint(3) / 5; dp[i][1] = mint(1) / 5; } } mat v; for(intmax_t i = 0; i < intmax_t(4 * n); i++) { v[i][0] = 0; } v[4 * n][0] = 1; cout << mul(pow(dp, k), v)[0][0]; }