#include #pragma region Header using i32 = int; using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using f64 = double; using f80 = long double; using f128 = __float128; constexpr i32 operator"" _i32(u64 v) { return v; } constexpr i32 operator"" _u32(u64 v) { return v; } constexpr i64 operator"" _i64(u64 v) { return v; } constexpr u64 operator"" _u64(u64 v) { return v; } constexpr f64 operator"" _f64(f80 v) { return v; } constexpr f80 operator"" _f80(f80 v) { return v; } using Istream = std::istream; using Ostream = std::ostream; using Str = std::string; template using Lt = std::less; template using Gt = std::greater; template using IList = std::initializer_list; template using BSet = std::bitset; template using Pair = std::pair; template using Tup = std::tuple; template using Arr = std::array; template using Deq = std::deque; template using Set = std::set; template using MSet = std::multiset; template using USet = std::unordered_set; template using UMSet = std::unordered_multiset; template using Map = std::map; template using MMap = std::multimap; template using UMap = std::unordered_map; template using UMMap = std::unordered_multimap; template using Vec = std::vector; template using Stack = std::stack; template using Queue = std::queue; template using MaxHeap = std::priority_queue; template using MinHeap = std::priority_queue, Gt>; using NSec = std::chrono::nanoseconds; using USec = std::chrono::microseconds; using MSec = std::chrono::milliseconds; using Sec = std::chrono::seconds; template constexpr T LIMMIN = std::numeric_limits::min(); template constexpr T LIMMAX = std::numeric_limits::max(); template constexpr T INF = (LIMMAX - 1) / 2; template constexpr T PI = T{3.141592653589793238462643383279502884}; template constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN(n - 1) * T{10}; } Ostream& operator<<(Ostream& os, i128 v) { bool minus = false; if (v < 0) { minus = true, v = -v; } Str ans; if (v == 0) { ans = "0"; } while (v) { ans.push_back('0' + v % 10), v /= 10; } std::reverse(ans.begin(), ans.end()); return os << (minus ? "-" : "") << ans; } Ostream& operator<<(Ostream& os, u128 v) { Str ans; if (v == 0) { ans = "0"; } while (v) { ans.push_back('0' + v % 10), v /= 10; } std::reverse(ans.begin(), ans.end()); return os << ans; } template bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } else { return false; } } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else { return false; } } template constexpr T fdiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? x / y : (x - y + 1) / y; } template constexpr T cdiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? (x + y - 1) / y : x / y; } template constexpr T modPower(T v, I n, T mod) { T ans = 1 % mod; for (; n > 0; n >>= 1, (v *= v) %= mod) { if (n % 2 == 1) { (ans *= v) %= mod; } } return ans; } template constexpr T power(T v, I n) { T ans = 1; for (; n > 0; n >>= 1, v *= v) { if (n % 2 == 1) { ans *= v; } } return ans; } template constexpr T power(T v, I n, const T& e) { T ans = e; for (; n > 0; n >>= 1, v *= v) { if (n % 2 == 1) { ans *= v; } } return ans; } template Vec operator+=(Vec& vs1, const Vec& vs2) { vs1.insert(vs1.end(), vs2.begin(), vs2.end()); return vs1; } template Vec operator+(const Vec& vs1, const Vec& vs2) { auto vs = vs1; vs += vs2; return vs; } template void fillAll(Vec& vs, const T& v) { std::fill(vs.begin(), vs.end(), v); } template> void sortAll(Vec& vs, C comp = C{}) { std::sort(vs.begin(), vs.end(), comp); } template void reverseAll(Vec& vs) { std::reverse(vs.begin(), vs.end()); } template void uniqueAll(Vec& vs) { sortAll(vs); vs.erase(std::unique(vs.begin(), vs.end()), vs.end()); } template V sumAll(const Vec& vs) { return std::accumulate(vs.begin(), vs.end(), V{}); } template int minInd(const Vec& vs) { return std::min_element(vs.begin(), vs.end()) - vs.begin(); } template int maxInd(const Vec& vs) { return std::max_element(vs.begin(), vs.end()) - vs.begin(); } template int lbInd(const Vec& vs, const T& v) { return std::lower_bound(vs.begin(), vs.end(), v) - vs.begin(); } template int ubInd(const Vec& vs, const T& v) { return std::upper_bound(vs.begin(), vs.end(), v) - vs.begin(); } template Vec genVec(int n, F gen) { Vec ans; std::generate_n(std::back_insert_iterator(ans), n, gen); return ans; } Vec iotaVec(int n, int offset = 0) { Vec ans(n); std::iota(ans.begin(), ans.end(), offset); return ans; } template Vec revVec(const Vec& vs) { auto ans = vs; reverseAll(ans); return ans; } constexpr int popcount(const u64 v) { return v ? __builtin_popcountll(v) : 0; } constexpr int log2p1(const u64 v) { return v ? 64 - __builtin_clzll(v) : 0; } constexpr int lsbp1(const u64 v) { return __builtin_ffsll(v); } constexpr int clog(const u64 v) { return v ? log2p1(v - 1) : 0; } constexpr u64 ceil2(const u64 v) { const int l = clog(v); return (l == 64) ? 0_u64 : (1_u64 << l); } constexpr u64 floor2(const u64 v) { return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64; } constexpr bool ispow2(const u64 v) { return (v > 0) and ((v & (v - 1)) == 0); } constexpr bool btest(const u64 mask, const int ind) { return (mask >> ind) & 1_u64; } template struct Fix : F { Fix(F&& f) : F{std::forward(f)} {} template auto operator()(Args&&... args) const { return F::operator()(*this, std::forward(args)...); } }; class irange { private: struct itr { itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {} bool operator!=(const itr& it) const { return m_cnt != it.m_cnt; } int operator*() { return m_cnt; } itr& operator++() { m_cnt += m_step; return *this; } i64 m_cnt, m_step; }; i64 m_start, m_end, m_step; public: irange(i64 start, i64 end, i64 step = 1) { assert(step != 0); const i64 d = std::abs(step); const i64 l = (step > 0 ? start : end); const i64 r = (step > 0 ? end : start); int n = (r - l) / d + ((r - l) % d ? 1 : 0); if (l >= r) { n = 0; } m_start = start; m_end = start + step * n; m_step = step; } itr begin() const { return itr{m_start, m_step}; } itr end() const { return itr{m_end, m_step}; } }; irange rep(int end) { return irange(0, end, 1); } irange per(int rend) { return irange(rend - 1, -1, -1); } #pragma COMMENT("[REFS] Xoshiro: https://prng.di.unimi.it") namespace xoshiro_impl { u64 x; u64 next() { uint64_t z = (x += 0x9e3779b97f4a7c15); z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9; z = (z ^ (z >> 27)) * 0x94d049bb133111eb; return z ^ (z >> 31); } } class Xoshiro32 { public: using result_type = u32; using T = result_type; Xoshiro32(T seed = 0) { xoshiro_impl::x = seed; s[0] = xoshiro_impl::next(); s[1] = xoshiro_impl::next(); s[2] = xoshiro_impl::next(); s[3] = xoshiro_impl::next(); } static constexpr T min() { return LIMMIN; } static constexpr T max() { return LIMMAX; } T operator()() { return next(); } private: static constexpr T rotl(const T x, int k) { return (x << k) | (x >> (32 - k)); } T next() { const T ans = rotl(s[1] * 5, 7) * 9; const T t = s[1] << 9; s[2] ^= s[0]; s[3] ^= s[1]; s[1] ^= s[2]; s[0] ^= s[3]; s[2] ^= t; s[3] = rotl(s[3], 11); return ans; } T s[4]; }; class Xoshiro64 { public: using result_type = u64; using T = result_type; Xoshiro64(T seed = 0) { xoshiro_impl::x = seed; s[0] = xoshiro_impl::next(); s[1] = xoshiro_impl::next(); s[2] = xoshiro_impl::next(); s[3] = xoshiro_impl::next(); } static constexpr T min() { return LIMMIN; } static constexpr T max() { return LIMMAX; } T operator()() { return next(); } private: static constexpr T rotl(const T x, int k) { return (x << k) | (x >> (64 - k)); } T next() { const T ans = rotl(s[1] * 5, 7) * 9; const T t = s[1] << 17; s[2] ^= s[0]; s[3] ^= s[1]; s[1] ^= s[2]; s[0] ^= s[3]; s[2] ^= t; s[3] = rotl(s[3], 45); return ans; } T s[4]; }; template class RNG { public: using result_type = typename Rng::result_type; using T = result_type; static constexpr T min() { return Rng::min(); } static constexpr T max() { return Rng::max(); } RNG() : RNG(std::random_device{}()) {} RNG(T seed) : m_rng(seed) {} T operator()() { return m_rng(); } template T val(T min, T max) { return std::uniform_int_distribution(min, max)(m_rng); } template Pair pair(T min, T max) { return std::minmax({val(min, max), val(min, max)}); } template Vec vec(int n, T min, T max) { return genVec(n, [&]() { return val(min, max); }); } template Vec> vvec(int n, int m, T min, T max) { return genVec>(n, [&]() { return vec(m, min, max); }); } private: Rng m_rng; }; RNG rng; RNG rng64; RNG rng_xo; RNG rng_xo64; class Scanner { public: Scanner(Istream& is = std::cin) : m_is{is} { m_is.tie(nullptr)->sync_with_stdio(false); } template T val() { T v; return m_is >> v, v; } template T val(T offset) { return val() - offset; } template Vec vec(int n) { return genVec(n, [&]() { return val(); }); } template Vec vec(int n, T offset) { return genVec(n, [&]() { return val(offset); }); } template Vec> vvec(int n, int m) { return genVec>(n, [&]() { return vec(m); }); } template Vec> vvec(int n, int m, const T offset) { return genVec>(n, [&]() { return vec(m, offset); }); } template auto tup() { return Tup{val()...}; } template auto tup(const Args&... offsets) { return Tup{val(offsets)...}; } private: Istream& m_is; }; Scanner in; class Printer { public: Printer(Ostream& os = std::cout) : m_os{os} { m_os << std::fixed << std::setprecision(15); } template int operator()(const Args&... args) { dump(args...); return 0; } template int ln(const Args&... args) { dump(args...), m_os << '\n'; return 0; } template int el(const Args&... args) { dump(args...), m_os << std::endl; return 0; } private: template void dump(const T& v) { m_os << v; } template void dump(const Vec& vs) { for (const int i : rep(vs.size())) { m_os << (i ? " " : ""), dump(vs[i]); } } template void dump(const Vec>& vss) { for (const int i : rep(vss.size())) { m_os << (i ? "\n" : ""), dump(vss[i]); } } template int dump(const T& v, const Ts&... args) { dump(v), m_os << ' ', dump(args...); return 0; } Ostream& m_os; }; Printer out; template auto ndVec(int const (&szs)[n], const T x = T{}) { if constexpr (i == n) { return x; } else { return std::vector(szs[i], ndVec(szs, x)); } } template T binSearch(T ng, T ok, F check) { while (std::abs(ok - ng) > 1) { const T mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; } template class modint { template static U modRef() { static u32 s_mod = 0; return s_mod; } template static U rootRef() { static u32 s_root = 0; return s_root; } template static U max2pRef() { static u32 s_max2p = 0; return s_max2p; } public: template static constexpr std::enable_if_t mod() { return mod_; } template static std::enable_if_t mod() { return modRef(); } template static constexpr std::enable_if_t root() { return root_; } template static std::enable_if_t root() { return rootRef(); } template static constexpr std::enable_if_t max2p() { return max2p_; } template static std::enable_if_t max2p() { return max2pRef(); } template static void setMod(std::enable_if_t m) { modRef() = m; } template static void setRoot(std::enable_if_t r) { rootRef() = r; } template static void setMax2p(std::enable_if_t m) { max2pRef() = m; } constexpr modint() : m_val{0} {} constexpr modint(i64 v) : m_val{normll(v)} {} constexpr void setRaw(u32 v) { m_val = v; } constexpr modint operator-() const { return modint{0} - (*this); } constexpr modint& operator+=(const modint& m) { m_val = norm(m_val + m.val()); return *this; } constexpr modint& operator-=(const modint& m) { m_val = norm(m_val + mod() - m.val()); return *this; } constexpr modint& operator*=(const modint& m) { m_val = normll((i64)m_val * (i64)m.val() % (i64)mod()); return *this; } constexpr modint& operator/=(const modint& m) { return *this *= m.inv(); } constexpr modint operator+(const modint& m) const { auto v = *this; return v += m; } constexpr modint operator-(const modint& m) const { auto v = *this; return v -= m; } constexpr modint operator*(const modint& m) const { auto v = *this; return v *= m; } constexpr modint operator/(const modint& m) const { auto v = *this; return v /= m; } constexpr bool operator==(const modint& m) const { return m_val == m.val(); } constexpr bool operator!=(const modint& m) const { return not(*this == m); } friend Istream& operator>>(Istream& is, modint& m) { i64 v; return is >> v, m = v, is; } friend Ostream& operator<<(Ostream& os, const modint& m) { return os << m.val(); } constexpr u32 val() const { return m_val; } template constexpr modint pow(I n) const { return power(*this, n); } constexpr modint inv() const { return pow(mod() - 2); } static modint sinv(u32 n) { static Vec is{1, 1}; for (u32 i = (u32)is.size(); i <= n; i++) { is.push_back(-is[mod() % i] * (mod() / i)); } return is[n]; } static modint fact(u32 n) { static Vec fs{1, 1}; for (u32 i = (u32)fs.size(); i <= n; i++) { fs.push_back(fs.back() * i); } return fs[n]; } static modint ifact(u32 n) { static Vec ifs{1, 1}; for (u32 i = (u32)ifs.size(); i <= n; i++) { ifs.push_back(ifs.back() * sinv(i)); } return ifs[n]; } static modint comb(int n, int k) { return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k); } private: static constexpr u32 norm(u32 x) { return x < mod() ? x : x - mod(); } static constexpr u32 normll(i64 x) { return norm(u32(x % (i64)mod() + (i64)mod())); } u32 m_val; }; using modint_1000000007 = modint<1000000007, 5, 1>; using modint_998244353 = modint<998244353, 3, 23>; template using modint_dynamic = modint<0, 0, id>; template class FPS : public Vec { public: using std::vector::vector; using std::vector::resize; FPS(const Vec& vs) : Vec{vs} {} int size() const { return Vec::size(); } int deg() const { return size() - 1; } FPS low(int n) const { return FPS{this->begin(), this->begin() + std::min(n, size())}; } FPS rev() const { FPS ans = *this; reverseAll(ans); return ans; } mint eval(const mint& x) const { mint ans = 0; mint power = 1; for (int i : rep(size())) { ans += power * (*this)[i]; power *= x; } return ans; } mint& operator[](const int n) { if (deg() < n) { resize(n + 1); } return Vec::operator[](n); } const mint& operator[](const int n) const { return Vec::operator[](n); } template mint at(const I n) const { return (n < size() ? (*this)[n] : mint{0}); } FPS operator-() const { FPS ans = *this; for (auto& v : ans) { v = -v; } return ans; } FPS& operator+=(const FPS& f) { for (int i : rep(f.size())) { (*this)[i] += f[i]; } return *this; } FPS& operator-=(const FPS& f) { for (int i : rep(f.size())) { (*this)[i] -= f[i]; } return *this; } FPS& operator*=(const FPS& f) { return (*this) = (*this) * f; } FPS& operator<<=(const int s) { return *this = (*this << s); } FPS& operator>>=(const int s) { return *this = (*this >> s); } FPS operator+(const FPS& f) const { return FPS(*this) += f; } FPS operator-(const FPS& f) const { return FPS(*this) -= f; } FPS operator*(const FPS& f) const { return mult(f, size() + f.size() - 1); } FPS operator<<(const int s) const { FPS ans(size() + s); for (int i : rep(size())) { ans[i + s] = (*this)[i]; } return ans; } FPS operator>>(const int s) const { FPS ans; for (int i : irange(s, size())) { ans[i - s] = (*this)[i]; } return ans; } friend Ostream& operator<<(Ostream& os, const FPS& f) { return os << static_cast>(f); } FPS derivative() const { FPS ans; for (int i : irange(1, size())) { ans[i - 1] = (*this)[i] * i; } return ans; } FPS integral() const { FPS ans; for (int i : irange(1, size() + 1)) { ans[i] = (*this)[i - 1] * mint::sinv(i); } return ans; } FPS mult(const FPS& f, int sz) const { if (sz == 0) { return FPS{}; } const int N = std::min(size(), sz) + std::min(f.size(), sz) - 1; if (N < 10) { FPS ans; for (int i : rep(sz)) { for (int j : rep(sz)) { if (i + j >= sz) { break; } ans[i + j] += this->at(i) * f.at(j); } } return ans; } if (N <= (1 << mint::max2p())) { auto ans = conv(*this, f, sz); return ans; } else { const auto cs1 = conv(*this, f, sz); const auto cs2 = conv(*this, f, sz); const auto cs3 = conv(*this, f, sz); FPS ans((int)cs1.size()); for (int i : rep(cs1.size())) { ans[i] = restore(cs1[i].val(), cs2[i].val(), cs3[i].val()); } return ans; } } FPS smult(int p, const mint a, int sz) { FPS ans = low(sz); for (int i = 0; i + p < sz; i++) { ans[i + p] += (*this)[i] * a; } return ans; } FPS sdiv(int p, const mint& a, int sz) { FPS ans = low(sz); for (int i = 0; i + p < sz; i++) { ans[i + p] -= ans[i] * a; } return ans; } FPS inv(int sz) const { const int n = size(); assert((*this)[0].val() != 0); const int N = n * 2 - 1; if (N <= (1 << mint::max2p())) { FPS r{(*this)[0].inv()}; for (int lg = 0, m = 1; m < sz; m <<= 1, lg++) { FPS f{this->begin(), this->begin() + std::min(n, 2 * m)}; FPS g = r; f.resize(2 * m), g.resize(2 * m); trans(f, lg + 1, false), trans(g, lg + 1, false); for (int i : rep(2 * m)) { f[i] *= g[i]; } trans(f, lg + 1, true); std::fill(f.begin(), f.begin() + m, 0); trans(f, lg + 1, false); for (int i : rep(2 * m)) { f[i] *= g[i]; } trans(f, lg + 1, true); for (int i = m; i < std::min(2 * m, sz); i++) { r[i] = -f[i]; } } return r; } else { FPS g{(*this)[0].inv()}; for (int lg = 0, m = 1; m < sz; m <<= 1, lg++) { g = FPS{2} * g - this->mult(g.mult(g, 2 * m), 2 * m); } return g.low(sz); } } FPS log(const int sz) const { assert((*this)[0].val() == 1); auto ans = derivative().mult(inv(sz), sz).integral(); ans.resize(sz); return ans; } FPS exp(const int sz) const { const int l = lsb(sz); if (l == -1) { return FPS{1}.low(sz); } assert((*this)[0].val() == 0); const int n = size(); const int N = n * 2 - 1; if (N <= (1 << mint::max2p())) { FPS f = {1, (*this)[1]}, g{1}, G{1, 1}; for (int m = 2, lg = 1; m < sz; m <<= 1, lg++) { auto F = f; F.resize(2 * m), trans(F, lg + 1, false); FPS z(m); for (int i : rep(m)) { z[i] = F[i] * G[i]; } trans(z, lg, true); std::fill(z.begin(), z.begin() + m / 2, 0); trans(z, lg, false); for (int i : rep(m)) { z[i] *= G[i]; } trans(z, lg, true); for (int i : irange(m / 2, m)) { g[i] = -z[i]; } G = g, G.resize(m * 2), trans(G, lg + 1, false); auto q = low(m).derivative(); q.resize(m), trans(q, lg, false); for (int i : rep(m)) { q[i] *= F[i]; } trans(q, lg, true); const auto df = f.derivative(); for (int i : rep(m - 1)) { q[i] -= df[i]; } q.resize(m * 2); for (int i : rep(m - 1)) { q[m + i] = q[i], q[i] = 0; } trans(q, lg + 1, false); for (int i : rep(m * 2)) { q[i] *= G[i]; } trans(q, lg + 1, true); q.pop_back(); q = q.integral(); for (int i = m; i < std::min(size(), m * 2); i++) { q[i] += (*this)[i]; } std::fill(q.begin(), q.begin() + m, 0); trans(q, lg + 1, false); for (int i = 0; i < m * 2; i++) { q[i] *= F[i]; } trans(q, lg + 1, true); for (int i = m; i < 2 * m; i++) { f[i] = q[i]; } } return f.low(sz); } else { FPS f{1}; for (int m = 1; m < sz; m <<= 1) { auto g = low(2 * m); g[0] += 1; f.resize(2 * m); g -= f.log(2 * m); g = f.mult(g, 2 * m); for (int i = m; i < std::min(2 * m, g.size()); i++) { f[i] = g[i]; } } return f.low(sz); } } template FPS pow(I n) const { return pow(n, deg() * n + 1); } template FPS pow(I n, int sz) const { if (n == 0) { return FPS{1}.low(sz); } if (size() == 0) { return FPS{}; } const int p = lsb(deg() / n); if (p == -1) { return FPS{}; } const mint a = (*this)[p]; FPS f = (*this) >> p; for (auto& c : f) { c /= a; } f = f.log(sz - p * n); for (auto& c : f) { c *= n; } f = f.exp(sz - p * n); FPS g; for (int i : rep(f.size())) { g[i + p * n] = f[i] * a.pow(n); } return g; } FPS tshift(const mint& c) const { const int N = size(); FPS f(N), d(N); for (int i = 0; i < N; i++) { d[i] = c.pow(N - 1 - i) * mint::ifact(N - 1 - i); } for (int i = 0; i < N; i++) { f[i] = (*this)[i] * mint::fact(i); } f = f * d; FPS g(N); for (int i = 0; i < N; i++) { g[i] = f[i + N - 1] * mint::ifact(i); } return g; } FPS quot(const FPS& g) const { const int N = size(), M = g.size(); if (N < M) { return FPS{}; } const auto fR = rev(), gR = g.rev(); return fR.mult(gR.inv(N - M + 1), N - M + 1).rev(); } FPS rem(const FPS& g) const { return (*this) - g * quot(g); } private: int lsb() const { return lsb(deg()); } int lsb(int sz) const { for (int p : rep(sz + 1)) { if ((*this)[p].val() != 0) { return p; } } return -1; } using submint1 = modint<469762049, 3, 26>; using submint2 = modint<167772161, 3, 25>; using submint3 = modint<754974721, 11, 24>; template static void trans(Vec& as, int lg, bool rev) { const int N = 1 << lg; assert((int)as.size() == N); Vec rs, irs; if (rs.empty()) { const submint r = submint(submint::root()), ir = r.inv(); rs.resize(submint::max2p() + 1), irs.resize(submint::max2p() + 1); rs.back() = -r.pow((submint::mod() - 1) >> submint::max2p()), irs.back() = -ir.pow((submint::mod() - 1) >> submint::max2p()); for (u32 i : irange(submint::max2p(), 0, -1)) { rs[i - 1] = -(rs[i] * rs[i]); irs[i - 1] = -(irs[i] * irs[i]); } } const auto drange = (rev ? irange(0, lg, 1) : irange(lg - 1, -1, -1)); for (const int d : drange) { const int width = 1 << d; submint e = 1; for (int i = 0, j = 1; i < N; i += width * 2, j++) { for (int l = i, r = i + width; l < i + width; l++, r++) { if (rev) { const submint x = as[l], y = as[r]; as[l] = x + y, as[r] = (x - y) * e; } else { const submint x = as[l], y = as[r] * e; as[l] = x + y, as[r] = x - y; } } e *= (rev ? irs : rs)[lsbp1(j) + 1]; } } if (rev) { const submint iN = submint{N}.inv(); for (auto& a : as) { a *= iN; } } } template static Vec conv(const Vec& as, const Vec& bs, int sz) { const int an = std::min((int)as.size(), sz); const int bn = std::min((int)bs.size(), sz); const int M = an + bn - 1; const int lg = clog(M); const int L = 1 << lg; Vec As(L), Bs(L); for (int i : rep(an)) { As[i] = as[i].val(); } for (int i : rep(bn)) { Bs[i] = bs[i].val(); } trans(As, lg, false), trans(Bs, lg, false); for (int i : rep(L)) { As[i] *= Bs[i]; } trans(As, lg, true); const int N = std::min(sz, (int)as.size() + (int)bs.size() - 1); As.resize(N); return As; } static constexpr submint2 ip1 = submint2{submint1::mod()}.inv(); static constexpr submint3 ip2 = submint3{submint2::mod()}.inv(); static constexpr submint3 ip1p2 = submint3{submint1::mod()}.inv() * ip2; static constexpr mint p1() { return mint{submint1::mod()}; } static constexpr mint p1p2() { return p1() * mint{submint2::mod()}; } static constexpr mint restore(int x1, int x2, int x3) { const int k0 = x1; const int k1 = (ip1 * (x2 - k0)).val(); const int k2 = (ip1p2 * (x3 - k0) - ip2 * k1).val(); return p1p2() * k2 + p1() * k1 + k0; } }; #pragma endregion int main() { constexpr uint P = 924844033; using mint = modint; const auto [A, B, C] = in.tup(); if ((A + B + C) % 2 == 1) { return out.ln(0); } const auto N = (A + B + C) / 2; mint ans = mint::comb(A + B + C, A) * mint::comb(B + C, B); void(0); const mint w = mint(5).pow((P - 1) / 3); FPS As; for (int a : rep(A + 1)) { As[a] = w.pow(2 * a + 2 * A) * mint::ifact(a) * mint::ifact(A - a); } FPS Bs; for (int b : rep(B + 1)) { Bs[b] = w.pow(b + B) * mint::ifact(b) * mint::ifact(B - b); } FPS Cs = As * Bs; mint sum = 0; for (int s : rep(N + 1)) { if (N - A - B + s < 0) { continue; } sum += mint::ifact(N - s) * mint::ifact(N - A - B + s) * Cs[s]; } sum *= mint::fact(N).pow(2); ans += sum * 2; ans /= 3; out.ln(ans); return 0; }