#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void)0 #endif // ============ #include #include #include // ============ constexpr bool is_prime(unsigned n) { if (n == 0 || n == 1) { return false; } for (unsigned i = 2; i * i <= n; ++i) { if (n % i == 0) { return false; } } return true; } constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) { unsigned ret = 1, self = x; while (y != 0) { if (y & 1) { ret = (unsigned) ((unsigned long long) ret * self % mod); } self = (unsigned) ((unsigned long long) self * self % mod); y /= 2; } return ret; } template constexpr unsigned primitive_root() { static_assert(is_prime(mod), "`mod` must be a prime number."); if (mod == 2) { return 1; } unsigned primes[32] = {}; int it = 0; { unsigned m = mod - 1; for (unsigned i = 2; i * i <= m; ++i) { if (m % i == 0) { primes[it++] = i; while (m % i == 0) { m /= i; } } } if (m != 1) { primes[it++] = m; } } for (unsigned i = 2; i < mod; ++i) { bool ok = true; for (int j = 0; j < it; ++j) { if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) { ok = false; break; } } if (ok) return i; } return 0; } // y >= 1 template constexpr T safe_mod(T x, T y) { x %= y; if (x < 0) { x += y; } return x; } // y != 0 template constexpr T floor_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return x / y; } else { return -((-x + y - 1) / y); } } // y != 0 template constexpr T ceil_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return (x + y - 1) / y; } else { return -(-x / y); } } // ============ template class ModInt { static_assert(mod != 0, "`mod` must not be equal to 0."); static_assert( mod < (1u << 31), "`mod` must be less than (1u << 31) = 2147483648."); unsigned val; public: static constexpr unsigned get_mod() { return mod; } constexpr ModInt() : val(0) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) (x % mod)) {} static constexpr ModInt raw(unsigned x) { ModInt ret; ret.val = x; return ret; } constexpr unsigned get_val() const { return val; } constexpr ModInt operator+() const { return *this; } constexpr ModInt operator-() const { return ModInt(0u) - *this; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if (val >= mod) val -= mod; return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { if (val < rhs.val) val += mod; val -= rhs.val; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { val = (unsigned long long)val * rhs.inv().val % mod; return *this; } friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) += rhs; } friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) /= rhs; } constexpr ModInt pow(unsigned long long x) const { ModInt ret = ModInt::raw(1); ModInt self = *this; while (x != 0) { if (x & 1) ret *= self; self *= self; x >>= 1; } return ret; } constexpr ModInt inv() const { static_assert(is_prime(mod), "`mod` must be a prime number."); assert(val != 0); return this->pow(mod - 2); } friend std::istream &operator>>(std::istream &is, ModInt &x) { long long val; is >> val; x.val = val % mod + (val < 0 ? mod : 0); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } friend bool operator==(const ModInt &lhs, const ModInt &rhs) { return lhs.val == rhs.val; } friend bool operator!=(const ModInt &lhs, const ModInt &rhs) { return lhs.val != rhs.val; } }; [[maybe_unused]] constexpr unsigned mod998244353 = 998244353; [[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007; // ============ // ============ #include #include template class FactorialTable { std::vector fac; std::vector ifac; public: FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {} FactorialTable(int n) : fac(n + 1), ifac(n + 1) { assert(n >= 0); fac[0] = T(1); for (int i = 1; i <= n; ++i) { fac[i] = fac[i - 1] * T(i); } ifac[n] = T(1) / T(fac[n]); for (int i = n; i > 0; --i) { ifac[i - 1] = ifac[i] * T(i); } } void resize(int n) { int old = n_max(); if (n <= old) { return; } fac.resize(n + 1); for (int i = old + 1; i <= n; ++i) { fac[i] = fac[i - 1] * T(i); } ifac.resize(n + 1); ifac[n] = T(1) / T(fac[n]); for (int i = n; i > old; --i) { ifac[i - 1] = ifac[i] * T(i); } } inline int n_max() const { return (int) fac.size() - 1; } inline T fact(int n) const { assert(n >= 0 && n <= n_max()); return fac[n]; } inline T inv_fact(int n) const { assert(n >= 0 && n <= n_max()); return ifac[n]; } inline T choose(int n, int k) const { assert(k <= n_max() && n <= n_max()); if (k > n || k < 0) { return T(0); } return fac[n] * ifac[k] * ifac[n - k]; } inline T multi_choose(int n, int k) const { assert(n >= 1 && k >= 0 && k + n - 1 <= n_max()); return choose(k + n - 1, k); } inline T n_terms_sum_k(int n, int k) const { assert(n >= 0); if (k < 0) { return T(0); } if (n == 0) { return k == 0 ? T(1) : T(0); } return choose(n + k - 1, n - 1); } }; // ============ using Mint = ModInt; int main() { i32 n, p; cin >> n >> p; FactorialTable table(n); Mint ans = table.fact(n); REP(i, n / p + 1) { i32 j = n - i * p; Mint ch = table.fact(n) / table.fact(min(n, p)).pow(i) / table.fact(i) / table.fact(j) * table.fact(min(n, p - 1)).pow(i); ans -= ch; } cout << ans << '\n'; }