#define _USE_MATH_DEFINES #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 dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, 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 val; MInt(): val(0) {} MInt(long long x) : val(x >= 0 ? x % MOD : x % MOD + MOD) {} static constexpr int get_mod() { return MOD; } static void set_mod(int divisor) { assert(divisor == MOD); } static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); } static MInt inv(int x, bool init = false) { // assert(0 <= x && x < MOD && std::__gcd(x, MOD) == 1); static std::vector inverse{0, 1}; int prev = inverse.size(); if (init && x >= prev) { // "x!" and "MOD" must be disjoint. inverse.resize(x + 1); for (int i = prev; i <= x; ++i) inverse[i] = -inverse[MOD % i] * (MOD / i); } if (x < inverse.size()) return inverse[x]; unsigned int a = x, b = MOD; int u = 1, v = 0; while (b) { unsigned int tmp = a / b; std::swap(a -= tmp * b, b); std::swap(u -= tmp * v, v); } return u; } static MInt fact(int x) { static std::vector f{1}; int prev = f.size(); if (x >= prev) { f.resize(x + 1); for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i; } return f[x]; } static MInt fact_inv(int x) { static std::vector finv{1}; int prev = finv.size(); if (x >= prev) { finv.resize(x + 1); finv[x] = inv(fact(x).val); for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i; } return finv[x]; } static MInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return 0; if (n - k > k) k = n - k; return fact(n) * fact_inv(k) * fact_inv(n - k); } static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } MInt pow(long long exponent) const { MInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } MInt &operator+=(const MInt &x) { if((val += x.val) >= MOD) val -= MOD; return *this; } MInt &operator-=(const MInt &x) { if((val += MOD - x.val) >= MOD) val -= MOD; return *this; } MInt &operator*=(const MInt &x) { val = static_cast(val) * x.val % MOD; return *this; } MInt &operator/=(const MInt &x) { return *this *= inv(x.val); } bool operator==(const MInt &x) const { return val == x.val; } bool operator!=(const MInt &x) const { return val != x.val; } bool operator<(const MInt &x) const { return val < x.val; } bool operator<=(const MInt &x) const { return val <= x.val; } bool operator>(const MInt &x) const { return val > x.val; } bool operator>=(const MInt &x) const { return val >= x.val; } MInt &operator++() { if (++val == MOD) val = 0; return *this; } MInt operator++(int) { MInt res = *this; ++*this; return res; } MInt &operator--() { val = (val == 0 ? MOD : val) - 1; return *this; } MInt operator--(int) { MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(val ? MOD - val : 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.val; } friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; } }; namespace std { template MInt abs(const MInt &x) { return x; } } using ModInt = MInt; template struct NTT { using ModInt = MInt; NTT() { for (int i = 0; i < 23; ++i) { if (primes[i][0] == ModInt::get_mod()) { n_max = 1 << primes[i][2]; root = ModInt(primes[i][1]).pow((ModInt::get_mod() - 1) >> primes[i][2]); return; } } assert(false); } void sub_dft(std::vector &a) { int n = a.size(); assert(__builtin_popcount(n) == 1); calc(n); int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n); for (int i = 0; i < n; ++i) { int j = butterfly[i] >> shift; if (i < j) std::swap(a[i], a[j]); } for (int block = 1; block < n; block <<= 1) { int den = __builtin_ctz(block); for (int i = 0; i < n; i += (block << 1)) for (int j = 0; j < block; ++j) { ModInt tmp = a[i + j + block] * omega[den][j]; a[i + j + block] = a[i + j] - tmp; a[i + j] += tmp; } } } template std::vector dft(const std::vector &a) { int n = a.size(), lg = 1; while ((1 << lg) < n) ++lg; std::vector A(1 << lg, 0); for (int i = 0; i < n; ++i) A[i] = a[i]; sub_dft(A); return A; } void idft(std::vector &a) { int n = a.size(); assert(__builtin_popcount(n) == 1); sub_dft(a); std::reverse(a.begin() + 1, a.end()); 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) { int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1; while ((1 << lg) < sz) ++lg; int n = 1 << lg; std::vector A(n, 0), B(n, 0); for (int i = 0; i < a_sz; ++i) A[i] = a[i]; for (int i = 0; i < b_sz; ++i) B[i] = b[i]; sub_dft(A); sub_dft(B); for (int i = 0; i < n; ++i) A[i] *= B[i]; idft(A); A.resize(sz); return A; } private: 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(int n) { int prev_n = butterfly.size(); if (n <= prev_n) return; assert(n <= n_max); butterfly.resize(n); int prev_lg = omega.size(), lg = __builtin_ctz(n); 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); ModInt tmp = root.pow((ModInt::get_mod() - 1) / (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; } } } }; int main() { int n, m, k; cin >> n >> m >> k; ModInt::init(n); int l = n - m; vector a(n - l + 1, 0), b(n - l + 1, 0); REP(i, n - l + 1) a[i] = ModInt::nCk(l + i - 1, i); for (int i = 0; i <= l && i * k <= n - l; ++i) b[i * k] = ModInt::nCk(l, i) * (i & 1 ? -1 : 1); vector c = NTT().convolution(a, b); ModInt ans = 0; for (int i = max(n - k + 1 - l, 0); i + l <= n && i < c.size(); ++i) ans += c[i]; cout << ans << '\n'; return 0; }