#include using namespace std; using int64 = long long; // const int mod = 1e9 + 7; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 1 "math/fft/fast-fourier-transform.cpp" namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector< C > rts = {{0, 0}, {1, 0}}; vector< int > rev = {0, 1}; void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while(base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector< C > &a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) { int need = (int) a.size() + (int) b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < sz; i++) { int x = (i < (int) a.size() ? a[i] : 0); int y = (i < (int) b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for(int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector< int64_t > ret(need); for(int i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } }; #line 2 "math/fft/arbitrary-mod-convolution.cpp" /* * @brief Arbitrary-Mod-Convolution(任意mod畳み込み) */ template< typename T > struct ArbitraryModConvolution { using real = FastFourierTransform::real; using C = FastFourierTransform::C; ArbitraryModConvolution() = default; static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) { if(need == -1) need = a.size() + b.size() - 1; int nbase = 0; while((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < a.size(); i++) { fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15); } fft(fa, sz); vector< C > fb(sz); if(a == b) { fb = fa; } else { for(int i = 0; i < b.size(); i++) { fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15); } fft(fb, sz); } real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if(i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector< T > ret(need); for(int i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa).x, bb = T(bb).x, cc = T(cc).x; ret[i] = aa + (bb << 15) + (cc << 30); } return ret; } }; #line 2 "math/fps/formal-power-series.cpp" /** * @brief Formal-Power-Series(形式的冪級数) */ template< typename T > struct FormalPowerSeries : vector< T > { using vector< T >::vector; using P = FormalPowerSeries; using Conv = ArbitraryModConvolution< T >; P pre(int deg) const { return P(begin(*this), begin(*this) + min((int) this->size(), deg)); } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } 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) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i]; return *this; } // https://judge.yosupo.jp/problem/convolution_mod P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } auto ret = Conv::multiply(*this, r); return *this = {begin(ret), end(ret)}; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P &operator%=(const P &r) { return *this -= *this / r * r; } // https://judge.yosupo.jp/problem/division_of_polynomials pair< P, P > div_mod(const P &r) { P q = *this / r; return make_pair(q, *this - q * r); } P operator-() const { P ret(this->size()); for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; return *this; } P &operator*=(const T &v) { for(int i = 0; i < this->size(); i++) (*this)[i] *= v; return *this; } P dot(P r) const { P ret(min(this->size(), r.size())); for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } P operator>>(int sz) const { if(this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } T operator()(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } P diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } P integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } // https://judge.yosupo.jp/problem/inv_of_formal_power_series // F(0) must not be 0 P inv(int deg = -1) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1) / (*this)[0]}); for(int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } return ret.pre(deg); } // https://judge.yosupo.jp/problem/log_of_formal_power_series // F(0) must be 1 P log(int deg = -1) const { assert((*this)[0] == T(1)); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const { const int n = (int) this->size(); if(deg == -1) deg = n; if((*this)[0] == T(0)) { for(int i = 1; i < n; i++) { if((*this)[i] != T(0)) { if(i & 1) return {}; if(deg - i / 2 <= 0) break; auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt); if(ret.empty()) return {}; ret = ret << (i / 2); if(ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); } auto sqr = T(get_sqrt((*this)[0])); if(sqr * sqr != (*this)[0]) return {}; P ret{sqr}; T inv2 = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg); } P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const { return sqrt(deg, get_sqrt); } // https://judge.yosupo.jp/problem/exp_of_formal_power_series // F(0) must be 0 P exp(int deg = -1) const { if(deg == -1) deg = this->size(); assert((*this)[0] == T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1)}); for(int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } // https://judge.yosupo.jp/problem/pow_of_formal_power_series P pow(int64_t k, int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k)); if(i * k > deg) return P(deg, T(0)); ret = (ret << (i * k)).pre(deg); if(ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return *this; } P mod_pow(int64_t k, P g) const { P modinv = g.rev().inv(); auto get_div = [&](P base) { if(base.size() < g.size()) { base.clear(); return base; } int n = base.size() - g.size() + 1; return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n); }; P x(*this), ret{1}; while(k > 0) { if(k & 1) { ret *= x; ret -= get_div(ret) * g; ret.shrink(); } x *= x; x -= get_div(x) * g; x.shrink(); k >>= 1; } return ret; } // https://judge.yosupo.jp/problem/polynomial_taylor_shift P taylor_shift(T c) const { int n = (int) this->size(); vector< T > fact(n), rfact(n); fact[0] = rfact[0] = T(1); for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i); rfact[n - 1] = T(1) / fact[n - 1]; for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i); P p(*this); for(int i = 0; i < n; i++) p[i] *= fact[i]; p = p.rev(); P bs(n, T(1)); for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1]; p = (p * bs).pre(n); p = p.rev(); for(int i = 0; i < n; i++) p[i] *= rfact[i]; return p; } }; template< typename Mint > using FPS = FormalPowerSeries< Mint >; template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; const int MOD = (int) (1e9 + 7); using mint = ModInt< MOD >; int main() { int64 N; int P, C; cin >> N >> P >> C; vector< int > as{2, 3, 5, 7, 11, 13}; vector< int > bs{4, 6, 8, 9, 10, 12}; auto gen = [&](vector< int > &xs, int sum) { auto dp = make_v< mint >(sum + 1, xs.back() * sum + 1); dp[0][0] = 1; for(int x : xs) { for(int i = 1; i <= sum; i++) { for(int j = x; j < dp[i].size(); j++) { dp[i][j] += dp[i - 1][j - x]; } } } return FPS< mint >{begin(dp[sum]), end(dp[sum])}; }; auto dp = gen(as, P) * gen(bs, C); dp[0] = -1; dp = dp.rev(); FPS< mint > x{0, 1}; auto cur = x.mod_pow(N + (int64) dp.size() - 2, dp); cout << accumulate(begin(cur), end(cur), mint(0)) << "\n"; }