#include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct MInt { unsigned int v; MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {} static constexpr int get_mod() { return M; } static void set_mod(const int divisor) { assert(divisor == M); } static void init(const int x) { inv(x); fact(x); fact_inv(x); } template static MInt inv(const int n) { // assert(0 <= n && n < M && std::gcd(n, M) == 1); static std::vector inverse{0, 1}; const int prev = inverse.size(); if (n < prev) return inverse[n]; if constexpr (MEMOIZES) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[M % i] * (M / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = M; b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector factorial{1}; const int prev = factorial.size(); if (n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector f_inv{1}; const int prev = f_inv.size(); if (n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) return 0; return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) return 0; inv(k); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if (std::cmp_greater_equal(v += x.v, M)) v -= M; return *this; } MInt& operator-=(const MInt& x) { if (std::cmp_greater_equal(v += M - x.v, M)) v -= M; return *this; } MInt& operator*=(const MInt& x) { v = static_cast(v) * x.v % M; return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } auto operator<=>(const MInt& x) const = default; MInt& operator++() { if (std::cmp_equal(++v, M)) v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? M - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(v ? M - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } }; using ModInt = MInt; template struct NumberTheoreticTransform { using ModInt = MInt; NumberTheoreticTransform() { for (int i = 0; i < 23; ++i) { if (primes[i][0] == ModInt::get_mod()) [[unlikely]] { n_max = 1 << primes[i][2]; root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]); return; } } assert(false); } template std::vector dft(const std::vector& a) { std::vector b(std::bit_ceil(a.size()), 0); std::copy(a.begin(), a.end(), b.begin()); calc(&b); return b; } void idft(std::vector* a) { assert(std::has_single_bit(a->size())); calc(a); std::reverse(std::next(a->begin()), a->end()); const int n = a->size(); const ModInt inv_n = ModInt::inv(n); for (int i = 0; i < n; ++i) { (*a)[i] *= inv_n; } } template std::vector convolution(const std::vector& a, const std::vector& b) { const int a_size = a.size(), b_size = b.size(); const int c_size = a_size + b_size - 1; const int n = std::bit_ceil(static_cast(c_size)); std::vector c(n, 0), d(n, 0); std::copy(a.begin(), a.end(), c.begin()); calc(&c); std::copy(b.begin(), b.end(), d.begin()); calc(&d); for (int i = 0; i < n; ++i) { c[i] *= d[i]; } idft(&c); c.resize(c_size); return c; } private: const int primes[23][3]{ {16957441, 329, 14}, {17006593, 26, 15}, {19529729, 770, 17}, {167772161, 3, 25}, {469762049, 3, 26}, {645922817, 3, 23}, {897581057, 3, 23}, {924844033, 5, 21}, {935329793, 3, 22}, {943718401, 7, 22}, {950009857, 7, 21}, {962592769, 7, 21}, {975175681, 17, 21}, {976224257, 3, 20}, {985661441, 3, 22}, {998244353, 3, 23}, {1004535809, 3, 21}, {1007681537, 3, 20}, {1012924417, 5, 21}, {1045430273, 3, 20}, {1051721729, 6, 20}, {1053818881, 7, 20}, {1224736769, 3, 24} }; int n_max; ModInt root; std::vector butterfly{0}; std::vector> omega{{1}}; void calc(std::vector* a) { const int n = a->size(), prev_n = butterfly.size(); if (n > prev_n) { assert(n <= n_max); butterfly.resize(n); const int prev_lg = omega.size(), lg = std::countr_zero(a->size()); for (int i = 1; i < prev_n; ++i) { butterfly[i] <<= lg - prev_lg; } for (int i = prev_n; i < n; ++i) { butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1)); } omega.resize(lg); for (int i = prev_lg; i < lg; ++i) { omega[i].resize(1 << i); const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1)); for (int j = 0; j < (1 << (i - 1)); ++j) { omega[i][j << 1] = omega[i - 1][j]; omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp; } } } const int shift = std::countr_zero(butterfly.size()) - std::countr_zero(a->size()); for (int i = 0; i < n; ++i) { const int j = butterfly[i] >> shift; if (i < j) std::swap((*a)[i], (*a)[j]); } for (int block = 1, den = 0; block < n; block <<= 1, ++den) { for (int i = 0; i < n; i += (block << 1)) { for (int j = 0; j < block; ++j) { const ModInt tmp = (*a)[i + j + block] * omega[den][j]; (*a)[i + j + block] = (*a)[i + j] - tmp; (*a)[i + j] += tmp; } } } } }; int main() { NumberTheoreticTransform ntt; int n; ll b, c; cin >> n >> b >> c; if (c > b) { cout << 0 << '\n'; return 0; } vector ways[2]{}; REP(parity, 2) { ways[parity].assign(n + 1, 0); for (int i = parity; i <= n; i += 2) { ways[parity][i] = ModInt::nCk(n, i); } } vector dp{1}; for (; b > 0; b >>= 1, c >>= 1) { dp = ntt.convolution(dp, ways[c & 1]); if (dp.size() > b + 1) dp.resize(b + 1); for (int i = (b & 1) ^ 1; i < dp.size(); i += 2) { dp[i] = 0; } FOR(i, 1, dp.size()) { dp[i / 2] += dp[i]; dp[i] = 0; } while (dp.size() > 1 && dp.back() == 0) dp.pop_back(); } cout << dp[0] << '\n'; return 0; }