Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/sum_of_exponential_times_polynomial.d63.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_exponential_times_polynomial"

#include "../../code/comb/gen_pows.hpp"
#include "../../code/math/sum_ipaf.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_d63.hpp"

using mint = tifa_libs::math::mint_d63<-1>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 r, d;
  u64 n;
  std::cin >> r >> d >> n;
  auto p = tifa_libs::math::gen_pows<mint>(d + 1, d);
  std::cout << tifa_libs::math::sum_ipaf(p, mint(r), n);
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/sum_of_exponential_times_polynomial.d63.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_exponential_times_polynomial"

#line 1 "src/code/comb/gen_pows.hpp"



#line 1 "src/code/math/qpow_mod.hpp"



#line 1 "src/code/math/mul_mod_u.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/math/mul_mod_u.hpp"

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 5 "src/code/math/qpow_mod.hpp"

namespace tifa_libs::math {

constexpr u64 qpow_mod(u64 a, u64 b, u64 mod) {
  u64 res(1);
  for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod))
    if (b & 1) res = mul_mod_u(res, a, mod);
  return res;
}

}  // namespace tifa_libs::math


#line 5 "src/code/comb/gen_pows.hpp"

namespace tifa_libs::math {

// i^{b} from i=0..n-1
constexpr vecu64 gen_pows(u32 n, u64 b, u64 mod) {
  vecu64 ans(n);
  if (!n) return {};
  if (!b) ans[0] = 1;
  if (n == 1) return ans;
  ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = qpow_mod(i, b, mod);
  return ans;
}
// i^{b} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_pows(u32 n, u64 b) {
  vec<mint> ans(n);
  auto _ = gen_pows(n, b, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/math/sum_ipaf.hpp"



#line 1 "src/code/comb/binom.hpp"



#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 1 "src/code/comb/gen_fact.hpp"



#line 5 "src/code/comb/gen_fact.hpp"

namespace tifa_libs::math {

// i! from i=0..n-1
constexpr vecu64 gen_fact(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(ans[i - 1], i, mod);
  return ans;
}
// i! from i=0..n-1
template <class mint>
constexpr vec<mint> gen_fact(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_fact(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/comb/gen_ifact.hpp"



#line 1 "src/code/comb/gen_inv.hpp"



#line 5 "src/code/comb/gen_inv.hpp"

namespace tifa_libs::math {

// i^{-1} from i=0..n-1
constexpr vecu64 gen_inv(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(mod - mod / i, ans[mod % i], mod);
  return ans;
}
// i^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_inv(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_inv(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/comb/gen_ifact.hpp"

namespace tifa_libs::math {

// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod, vecu64 inv) {
  for (u32 i = 2; i < n; ++i) inv[i] = mul_mod_u(inv[i], inv[i - 1], mod);
  return inv;
}
// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod) { return gen_ifact(n, mod, gen_inv(n, mod)); }
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n, vec<mint> inv) {
  for (u32 i = 2; i < n; ++i) inv[i] *= inv[i - 1];
  return inv;
}
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n) { return gen_ifact(n, gen_inv<mint>(n)); }

}  // namespace tifa_libs::math


#line 7 "src/code/comb/binom.hpp"

namespace tifa_libs::math {

template <class mint>
struct Binom {
  const vec<mint> fact, ifact;

  explicit constexpr Binom(u32 max_m) : fact(gen_fact<mint>(max_m + 1)), ifact(gen_ifact<mint>(max_m + 1)) {}

  static constexpr u64 mod() { return mint::mod(); }

  // \binom{m}{n}
  template <uint_c T>
  constexpr mint mCn(T m, T n) const { return m < n ? 0 : mPn(m, n) * ifact[(usz)n]; }
  // \binom{m}{n}
  template <sint_c T>
  constexpr mint mCn(T m, T n) const { return m < n || n < 0 ? 0 : mCn(to_uint_t<T>(m), to_uint_t<T>(n)); }

  // \binom{m}{n} * n!
  template <uint_c T>
  constexpr mint mPn(T m, T n) const { return m < n ? 0 : fact[(usz)m] * ifact[(usz)(m - n)]; }
  // \binom{m}{n} * n!
  template <sint_c T>
  constexpr mint mPn(T m, T n) const { return m < n || n < 0 ? 0 : mPn(to_uint_t<T>(m), to_uint_t<T>(n)); }

  // [x^n] 1 / (1-x)^m
  template <uint_c T>
  constexpr mint mHn(T m, T n) const { return n <= 0 ? n == 0 : mCn(m + n - 1, n); }
  // [x^n] 1 / (1-x)^m
  template <sint_c T>
  constexpr mint mHn(T m, T n) const { return m < 0 || n <= 0 ? n == 0 : mHn(to_uint_t<T>(m), to_uint_t<T>(n)); }
};

}  // namespace tifa_libs::math


#line 1 "src/code/math/lagrange_interp0.hpp"



#line 1 "src/code/math/mul_mod_s.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 5 "src/code/math/mul_mod_s.hpp"

namespace tifa_libs::math {

constexpr i64 mul_mod_s(i64 a, i64 b, u64 mod) {
  if (std::bit_width((u64)abs(a)) + std::bit_width((u64)abs(b)) < 64) return safe_mod(a * b % (i64)mod, mod);
  else return safe_mod((i64)((i128)a * b % mod), mod);
}

}  // namespace tifa_libs::math


#line 7 "src/code/math/lagrange_interp0.hpp"

namespace tifa_libs::math {

constexpr i64 lagrange_interp0(vec<i64> const &v, u64 x, u64 mod, vecu64 const &ifact) {
  u32 n = (u32)v.size();
  assert(n);
  if (n == 1) return v[0];
  if (x < n) return v[x];
  vecu64 pre(n);
  for (u32 i = 0; i < n; ++i) pre[i] = x - i;
  for (u32 i = 1; i < n; ++i) pre[i] = mul_mod_u(pre[i], pre[i - 1], mod);
  vecu64 suc(n);
  for (u32 i = 0; i < n; ++i) suc[i] = x - i;
  for (u32 i = n - 2; ~i; --i) suc[i] = mul_mod_u(suc[i], suc[i + 1], mod);
  i64 ans = 0;
  for (u32 i = 0; i < n; ++i) {
    i64 _ = v[i];
    if (i) _ = mul_mod_s(_, (i64)pre[i - 1], mod);
    if (i + 1 < n) _ = mul_mod_s(_, (i64)suc[i + 1], mod);
    _ = mul_mod_s(mul_mod_s(_, (i64)ifact[i], mod), (i64)ifact[n - i - 1], mod);
    ans = (ans + ((n - i) % 2 ? _ : (i64)mod - _)) % (i64)mod;
  }
  return ans;
}
constexpr i64 lagrange_interp0(vec<i64> const &v, u64 x, u64 mod) { return lagrange_interp0(v, x, mod, gen_ifact((u32)v.size(), mod)); }
template <class mint>
constexpr mint lagrange_interp0(vec<mint> const &v, u64 x, vec<mint> const &ifact) {
  vec<i64> _(v.size());
  for (u32 i = 0; i < (u32)v.size(); ++i) _[i] = v[i].val();
  vecu64 ifa(ifact.size());
  for (u32 i = 0; i < (u32)ifact.size(); ++i) ifa[i] = ifact[i].val();
  return mint(lagrange_interp0(_, x, mint::mod(), ifa));
}
template <class mint>
constexpr mint lagrange_interp0(vec<mint> const &v, u64 x) { return lagrange_interp0(v, x, mint::mod(), gen_ifact<mint>(v.size())); }

}  // namespace tifa_libs::math


#line 1 "src/code/math/qpow.hpp"



#line 5 "src/code/math/qpow.hpp"

namespace tifa_libs::math {

template <class T>
constexpr T qpow(T a, u64 b, T const& init_v = T{1}) {
  T res = init_v;
  for (; b; b >>= 1, a = a * a)
    if (b & 1) res = res * a;
  return res;
}

}  // namespace tifa_libs::math


#line 7 "src/code/math/sum_ipaf.hpp"

namespace tifa_libs::math {

// @param f $f(0),\dots,f(k-1)$, $k\leq n$
// @return $\sum_{i=0}^{n-1}a^if(i)$
template <class mint>
constexpr mint sum_ipaf(vec<mint> const& f, mint const& a, u64 n, Binom<mint> const& C) {
  if (!n) return mint(0);
  if (!a.val()) return f[0];
  if (a.val() == 1) {
    vec<mint> g(f.size() + 1, mint(0));
    for (u32 i = 1; i < g.size(); ++i) g[i] = g[i - 1] + f[i - 1];
    return lagrange_interp0(g, n, C.ifact);
  }
  vec<mint> g(f.size());
  mint buf = 1;
  for (u32 i = 0; i < g.size(); ++i) g[i] = f[i] * buf, buf *= a;
  for (u32 i = 1; i < g.size(); ++i) g[i] += g[i - 1];
  mint c = 0, buf2 = 1;
  u32 K = u32(f.size() - 1);
  for (u32 i = 0; i <= K; ++i) c += C.mCn(K + 1, i) * buf2 * g[K - i], buf2 *= -a;
  c /= qpow(-a + 1, K + 1);
  mint buf3 = 1, ia = a.inv();
  for (u32 i = 0; i < g.size(); ++i) g[i] = (g[i] - c) * buf3, buf3 *= ia;
  return lagrange_interp0(g, n - 1, C.ifact) * qpow(a, n - 1) + c;
}
template <class mint>
constexpr mint sum_ipaf(vec<mint> const& f, mint const& a, u64 n) {
  if (!n) return mint(0);
  if (!a.val()) return f[0];
  return sum_ipaf(f, a, n, Binom<mint>((u32)(f.size() + 1)));
}

}  // namespace tifa_libs::math


#line 6 "src/test_cpverifier/library-checker/sum_of_exponential_times_polynomial.d63.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_d63.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_d63.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d63 : public mint<mint_d63<ID>, u64> {
  using base = mint<mint_d63<ID>, u64>;
  friend base;

  static inline u64 MOD, R, R2;

  static constexpr u64 mul_h(u64 x, u64 y) {
    u64 a = x >> 32, b = (u32)x, c = y >> 32, d = (u32)y, ad = a * d, bc = b * c;
    return a * c + (ad >> 32) + (bc >> 32) + (((ad & 0xFFFFFFFF) + (bc & 0xFFFFFFFF) + (b * d >> 32)) >> 32);
  }
  static constexpr u64 redc_mul(u64 x, u64 y) {
    u64 res = mul_h(x, y) - mul_h(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return u64(x + i64(MOD & u64(-(x < 0)))); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u64 m) {
    assert(!((m & 1) == 0 || m == 1 || m >> 63));
    MOD = m;
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    R = iv * (t - MOD * iv);
    R2 = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((R2 *= 2) >= MOD) R2 -= MOD;
  }

  constexpr mint_d63() {}
  template <int_c T>
  constexpr mint_d63(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return redc_mul(norm(i64(v % (std::conditional_t<sint_c<T>, i64, u64>)mod_())), R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t res = -mul_h(this->v_ * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d63 neg_() const {
    mint_d63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_d63 &adde_(mint_d63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &sube_(mint_d63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &mule_(mint_d63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 10 "src/test_cpverifier/library-checker/sum_of_exponential_times_polynomial.d63.test.cpp"

using mint = tifa_libs::math::mint_d63<-1>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 r, d;
  u64 n;
  std::cin >> r >> d >> n;
  auto p = tifa_libs::math::gen_pows<mint>(d + 1, d);
  std::cout << tifa_libs::math::sum_ipaf(p, mint(r), n);
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 0_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 0_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 0_02 :heavy_check_mark: AC 1482 ms 160 MB
g++-12 0_03 :heavy_check_mark: AC 1482 ms 160 MB
g++-12 0_04 :heavy_check_mark: AC 1483 ms 160 MB
g++-12 1_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 1_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 1_02 :heavy_check_mark: AC 8 ms 4 MB
g++-12 1_03 :heavy_check_mark: AC 2426 ms 628 MB
g++-12 1_04 :heavy_check_mark: AC 1482 ms 160 MB
g++-12 1_05 :heavy_check_mark: AC 1926 ms 472 MB
g++-12 1_06 :heavy_check_mark: AC 2273 ms 628 MB
g++-12 2_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 2_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 2_02 :heavy_check_mark: AC 8 ms 4 MB
g++-12 2_03 :heavy_check_mark: AC 2803 ms 628 MB
g++-12 2_04 :heavy_check_mark: AC 1492 ms 160 MB
g++-12 2_05 :heavy_check_mark: AC 2432 ms 472 MB
g++-12 2_06 :heavy_check_mark: AC 2778 ms 628 MB
g++-12 example_00 :heavy_check_mark: AC 7 ms 4 MB
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