// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector &v, vector const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template auto prefix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template auto suffix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template T pop(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop(priority_queue &a) { auto x = a.top(); a.pop(); return x; } template T pop(queue &a) { auto x = a.front(); a.pop(); return x; } template T pop_front(deque &a) { auto x = a.front(); a.pop_front(); return x; } template T pop_back(deque &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_front(set &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template T pop_back(set &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template T pop_front(multiset &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template T pop_back(multiset &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 and n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< constexpr int64_t MOD = 998244353; //constexpr int64_t MOD = 1e9+7; using mint = modint; mint sign(int n) { return n & 1 ? -1 : +1; } // >>> mod table template struct ModTable { vector fact, finv; void calc(int n) { int old = fact.size(); if (n < old) return; n += 1000; fact.resize(n+1); finv.resize(n+1); if (old == 0) { fact[0] = fact[1] = finv[0] = finv[1] = 1; old = 2; } for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i; finv[n] = mint(1) / fact[n]; for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1); } }; ModTable mod_tab; mint fact(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.fact[n]; } mint finv(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.finv[n]; } mint comb(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k]; } mint perm(int n, int k) { assert(k >= 0); assert(n >= k); mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[n-k]; } // <<< // >>> FPS template struct FormalPowerSeries : NTT, vector { using mint = typename NTT::modint; using NTT::conv; using vector::vector; // inherit constructors using FPS = FormalPowerSeries; FormalPowerSeries() : vector() {} FormalPowerSeries(vector const& v) : vector(v) {} FormalPowerSeries(mint const& x) : vector({x}) {} void shrink() { while (this->size() and this->back() == 0) this->pop_back(); } mint get(int i) const { assert(i >= 0); if (i < (int)this->size()) return (*this)[i]; else return 0; } mint &set(int i, mint x) { assert(i >= 0); if (i >= (int)this->size()) this->resize(i+1); return (*this)[i] = x; } bool operator==(FPS const& r) const { const int n = min(this->size(), r.size()); rep (i, n) { if ((*this)[i] != r[i]) return false; } for (int i = n; i < (int)this->size(); ++i) { if ((*this)[i] != mint(0)) return false; } for (int i = n; i < (int)r.size(); ++i) { if (r[i] != mint(0)) return false; } return true; } bool operator!=(FPS const& r) const { return !((*this) == r); } FPS operator+(FPS const& r) const { return FPS(*this) += r; } FPS operator-(FPS const& r) const { return FPS(*this) -= r; } FPS& operator+=(FPS const& r) { if (r.size() > this->size()) this->resize(r.size()); rep (i, r.size()) (*this)[i] += r[i]; return *this; } FPS& operator-=(FPS const& r) { if (r.size() > this->size()) this->resize(r.size()); rep (i, r.size()) (*this)[i] -= r[i]; return *this; } FPS operator*(FPS const& r) const { if (this->empty() || r.empty()) return {}; return conv(*this, r); } FPS& operator*=(FPS const& r) { return *this = *this * r; } friend FPS operator+(mint const& x, FPS const& f) { return FPS{x}+f; } friend FPS operator-(mint const& x, FPS const& f) { return FPS{x}-f; } friend FPS operator*(mint const& x, FPS const& f) { return FPS{x}*f; } friend FPS operator+(FPS const& f, mint const& x) { return f+FPS{x}; } friend FPS operator-(FPS const& f, mint const& x) { return f-FPS{x}; } friend FPS operator*(FPS const& f, mint const& x) { return f*FPS{x}; } FPS take(int sz) const { FPS ret(this->begin(), this->begin() + min(this->size(), sz)); ret.resize(sz); return ret; } FPS inv(int sz = -1) const { assert(this->size()); assert((*this)[0] != mint(0)); if (sz < 0) sz = this->size(); FPS ret = { mint(1)/(*this)[0] }; for (int i = 1; i < sz; i <<= 1) { ret = ret + ret - ret*ret*take(i<<1); ret.resize(i<<1); } ret.resize(sz); return ret; } FPS diff() const { FPS ret(max(0, this->size()-1)); rep (i, ret.size()) ret[i] = (*this)[i+1]*mint(i+1); return ret; } FPS integral() const { FPS ret(this->size()+1); ret[0] = 0; rep (i, this->size()) ret[i+1] = (*this)[i]/mint(i+1); return ret; } FPS log(int sz = -1) const { assert(this->size()); assert((*this)[0] == mint(1)); if (sz < 0) sz = this->size(); return (diff()*inv(sz)).take(sz-1).integral(); } // FPS log(int sz = -1) const { // assert(this->size()); assert((*this)[0] == mint(1)); // if (sz < 0) sz = this->size(); // auto ret = diff()*inv(sz); // ret.resize(sz); // for (int i = sz-1; i > 0; --i) ret[i] = ret[i-1]/mint(i); // ret[0] = 0; // return ret; // } FPS exp(int sz = -1) const { FPS ret = {mint(1)}; if (this->empty()) return ret; assert((*this)[0] == mint(0)); if (sz < 0) sz = this->size(); for (int i = 1; i < sz; i <<= 1) { ret *= take(i<<1) + mint(1) - ret.log(i<<1); ret.resize(i<<1); } ret.resize(sz); return ret; } FPS pow(int64_t k, int sz = -1) const { if (sz < 0) sz = this->size(); int deg = 0; while (deg < sz && (*this).get(deg) == mint(0)) ++deg; assert(k >= 0 || deg == 0); auto c = mint(1)/(*this).get(deg); FPS ret(sz-deg); rep (i, sz-deg) ret[i] = (*this).get(deg+i)*c; ret = (ret.log()*k).exp() * (*this).get(deg).pow(k); ret.resize(sz); for (int i = sz-1; i >= 0; --i) { int j = i-deg*k; ret[i] = (j >= 0 ? ret[j] : mint(0)); } return ret; } mint eval(mint x) const { mint p = 1, ret = 0; rep (i, this->size()) { ret += (*this)[i] * p; p *= x; } return ret; } }; // <<< // >>> NTT template struct NTT { using modint = ModInt; static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1); // mod:prime, g:primitive root static_assert(mod > 0 && g > 0 && max_lg > 0, ""); using arr_t = array; static arr_t ws, iws; static void init() { static bool built = false; if (built) return; for (int i = 0; i <= max_lg; i++) { ws[i] = -ModInt(g).pow((mod-1)>>(i+2)); iws[i] = ModInt(1)/ws[i]; } built = true; } static void ntt(ModInt a[], int lg) { for (int b = lg-1; b >= 0; b--) { ModInt w = 1; for (int i = 0, k = 0; i < (1< static vector conv(vector const& a, vector const& b) { if (a.empty() || b.empty()) return {}; init(); const int s = a.size() + b.size() - 1, lg = __lg(2*s-1); assert(lg <= max_lg); vector aa(1< bb(1< static vector conv(vector const& a) { if (a.empty()) return {}; init(); const int s = a.size()*2 - 1, lg = __lg(2*s-1); assert(lg <= max_lg); vector aa(1< typename NTT::arr_t NTT::ws; template typename NTT::arr_t NTT::iws; // <<< using ntt = NTT; using FPS = FormalPowerSeries; int32_t main() { int n; cin >> n; mint p, q; { mint a, b; cin >> a >> b; p = a/b; q = 1-p; } vector g0(n), g1(n); g0[0] = FPS { 0, 1 }; g1[0] = FPS { 1, 0 }; rep (i, n-1) { g0[i+1] = g0[i] * (g0[i] + 2*p*g1[i]); g1[i+1] = g1[i] * (g1[i] + 2*q*g0[i]); dump(i+1); dump(g0[i+1]); dump(g1[i+1]); } FPS f = { 1 }; rep (i, n) f *= q*g0[i] + p*g1[i]; dump(f); rep (i, 1LL<