結果

問題 No.117 組み合わせの数
ユーザー KowerKoint2010KowerKoint2010
提出日時 2023-09-16 00:06:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 241 ms / 5,000 ms
コード長 32,883 bytes
コンパイル時間 1,779 ms
コンパイル使用メモリ 99,412 KB
最終ジャッジ日時 2025-02-16 22:44:54
ジャッジサーバーID
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judge4 / judge4
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#line 1 "test/yukicoder-117.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/117"
#line 2 "cpp/combinatorics.hpp"
#include <vector>
#line 2 "cpp/number-theory.hpp"
#include <numeric>
#line 2 "cpp/modint.hpp"
/**
* @file modint.hpp
* @brief mod
*/
#include <iostream>
#include <utility>
#include <limits>
#include <type_traits>
#include <cstdint>
#include <cassert>
namespace detail {
static constexpr std::uint16_t prime32_bases[] {
15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560, 3128, 5212, 2657,
2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763, 4852, 5012,
3185, 1333, 6227, 5298, 1074, 2391, 5113, 7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239,
746, 2951, 556, 2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344,
17, 15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903, 737, 1887,
7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875, 3110, 13221, 8726, 571,
7043, 6943, 1199, 352, 6435, 165, 1169, 3315, 978, 233, 3003, 2562, 2994, 10587, 10030, 2377,
1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784,
1661, 524, 3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031, 2226,
2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336, 579, 165, 1375, 10018,
12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727, 3639, 1595, 4944,
2129, 2029, 8195, 8344, 6232, 9183, 8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566,
5674, 411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785,
1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42, 4511, 1660, 166,
1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197, 13330, 7054, 2818, 3199, 811,
922, 350, 7514, 4452, 3449, 2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194,
};
static constexpr bool is_SPRP(std::uint32_t n, std::uint32_t a) noexcept {
std::uint32_t d = n - 1;
std::uint32_t s = 0;
while ((d & 1) == 0) {
++s;
d >>= 1;
}
std::uint64_t cur = 1;
std::uint64_t pw = d;
while (pw) {
if (pw & 1) cur = (cur * a) % n;
a = (static_cast<std::uint64_t>(a) * a) % n;
pw >>= 1;
}
if (cur == 1) return true;
for (std::uint32_t r = 0; r < s; ++r) {
if (cur == n - 1) return true;
cur = (cur * cur) % n;
}
return false;
}
// 32
// : M. Forisek and J. Jancina, “Fast Primality Testing for Integers That Fit into a Machine Word,” presented at the Conference on Current
        Trends in Theory and Practice of Informatics, 2015.
[[nodiscard]]
static constexpr bool is_prime32(std::uint32_t x) noexcept {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
std::uint64_t h = x;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) & 0xff;
return is_SPRP(x, prime32_bases[h]);
}
}
/// @brief static_modint dynamic_modint CRTP
/// @tparam Modint
template <class Modint>
class modint_base {
public:
/// @brief
using value_type = std::uint32_t;
/// @brief 0
constexpr modint_base() noexcept
: m_value{ 0 } {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral> && std::is_signed_v<SignedIntegral>>* = nullptr>
constexpr modint_base(SignedIntegral value) noexcept
: m_value{ static_cast<value_type>((static_cast<long long>(value) % Modint::mod() + Modint::mod()) % Modint::mod()) } {}
/// @brief @c value
/// @param value 使
template <class UnsignedIntegral, std::enable_if_t<std::is_integral_v<UnsignedIntegral> && std::is_unsigned_v<UnsignedIntegral>>* = nullptr>
constexpr modint_base(UnsignedIntegral value) noexcept
: m_value{ static_cast<value_type>(value % Modint::mod()) } {}
/// @brief
/// @return
[[nodiscard]]
constexpr value_type value() const noexcept {
return m_value;
}
/// @brief
/// @return @c *this
constexpr Modint& operator++() noexcept {
++m_value;
if (m_value == Modint::mod()) {
m_value = 0;
}
return static_cast<Modint&>(*this);
}
/// @brief
/// @return @c *this
constexpr Modint operator++(int) noexcept {
auto x = static_cast<const Modint&>(*this);
++*this;
return x;
}
/// @brief
/// @return @c *this
constexpr Modint& operator--() noexcept {
if (m_value == 0) {
m_value = Modint::mod();
}
--m_value;
return static_cast<Modint&>(*this);
}
/// @brief
/// @return @c *this
constexpr Modint operator--(int) noexcept {
auto x = static_cast<const Modint&>(*this);
--*this;
return x;
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator+=(const Modint& x) noexcept {
m_value += x.m_value;
if (m_value >= Modint::mod()) {
m_value -= Modint::mod();
}
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator-=(const Modint& x) noexcept {
m_value -= x.m_value;
if (m_value >= Modint::mod()) {
m_value += Modint::mod();
}
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator*=(const Modint& x) noexcept {
m_value = static_cast<value_type>(static_cast<std::uint64_t>(m_value) * x.m_value % Modint::mod());
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @remark @f$O(\log x)@f$
/// @param x
/// @return @c *this
constexpr Modint& operator/=(const Modint& x) noexcept {
return *this *= x.inv();
}
/// @brief
/// @return @c *this
[[nodiscard]]
constexpr Modint operator+() const noexcept {
return static_cast<const Modint&>(*this);
}
/// @brief
/// @return
[[nodiscard]]
constexpr Modint operator-() const noexcept {
return 0 - static_cast<const Modint&>(*this);
}
/// @brief @c n
/// @remark @f$O(\log n)@f$
/// @param n
/// @return @c n
[[nodiscard]]
constexpr Modint pow(unsigned long long n) const noexcept {
Modint x = 1;
Modint y = static_cast<const Modint&>(*this);
while (n) {
if (n & 1) {
x *= y;
}
y *= y;
n >>= 1;
}
return x;
}
/// @brief
/// @remark @f$O(\log value)@f$
/// @return
[[nodiscard]]
constexpr Modint inv() const noexcept {
long long a = Modint::mod();
long long b = m_value;
long long x = 0;
long long y = 1;
while (b) {
auto t = a / b;
auto u = a - t * b;
a = b;
b = u;
u = x - t * y;
x = y;
y = u;
}
assert(a == 1 && "The inverse element does not exist.");
x %= Modint::mod();
if (x < 0) {
x += Modint::mod();
}
return x;
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator+(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } += y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator-(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } -= y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator*(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } *= y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator/(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } /= y);
}
/// @brief @c x @c y 調
/// @return @c x @c y @c true @c false
[[nodiscard]]
friend constexpr bool operator==(const Modint& x, const Modint& y) noexcept {
return x.m_value == y.m_value;
}
/// @brief @c x @c y 調
/// @return @c x @c y @c false @c true
[[nodiscard]]
friend constexpr bool operator!=(const Modint& x, const Modint& y) noexcept {
return not (x == y);
}
/// @brief @c x
/// @tparam CharT
/// @tparam Traits
/// @param is
/// @param x
/// @return @c is
template <class CharT, class Traits>
friend std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, Modint& x) {
long long tmp;
is >> tmp;
x = tmp;
return is;
}
/// @brief @c x
/// @tparam CharT
/// @tparam Traits
/// @param os
/// @param x
/// @return @c os
template <class CharT, class Traits>
friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const Modint& x) {
os << x.value();
return os;
}
protected:
value_type m_value;
};
/// @brief mod
/// @tparam Mod
template <std::uint32_t Mod>
class static_modint : public modint_base<static_modint<Mod>> {
static_assert(Mod > 0 && Mod <= std::numeric_limits<std::uint32_t>::max() / 2);
private:
using base_type = modint_base<static_modint<Mod>>;
public:
using typename base_type::value_type;
/// @brief
/// @return
[[nodiscard]]
static constexpr value_type mod() noexcept {
return Mod;
}
/// @brief 0
constexpr static_modint() noexcept
: base_type{} {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
constexpr static_modint(SignedIntegral value) noexcept
: base_type{value} {}
/// @brief
/// @remark @f$O(\log value)@f$
/// @return
[[nodiscard]]
constexpr static_modint inv() const noexcept {
if constexpr (detail::is_prime32(Mod)) {
assert(this->m_value != 0 && "The inverse element of zero does not exist.");
return this->pow(Mod - 2);
}
else {
return base_type::inv();
}
}
};
/// @brief mod
/// @tparam ID ID
template <int ID>
class dynamic_modint : public modint_base<dynamic_modint<ID>> {
private:
using base_type = modint_base<dynamic_modint<ID>>;
public:
using typename base_type::value_type;
/// @brief
/// @return
[[nodiscard]]
static value_type mod() noexcept {
return modulus;
}
/// @brief
/// @param m
static void set_mod(value_type m) noexcept {
assert(m > 0 && m <= std::numeric_limits<value_type>::max() / 2);
modulus = m;
}
/// @brief 0
constexpr dynamic_modint() noexcept
: base_type{} {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
constexpr dynamic_modint(SignedIntegral value) noexcept
: base_type{value} {}
private:
inline static value_type modulus = 998244353;
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
#line 6 "cpp/number-theory.hpp"
/**
* @brief a^(-1) mod MOD
* @param a long long
* @param MOD long long
* @return long long
*/
long long modinv(long long a, long long MOD) {
long long b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= MOD;
if (u < 0) u += MOD;
return u;
}
/**
* @brief a^n mod MOD
* @param a long long
* @param n long long
* @param MOD long long
* @return long long
*/
long long modpow(long long a, long long n, long long MOD) {
long long res = 1;
a %= MOD;
if(n < 0) {
n = -n;
a = modinv(a, MOD);
}
while (n > 0) {
if (n & 1) res = res * a % MOD;
a = a * a % MOD;
n >>= 1;
}
return res;
}
/**
* @brief 2m
* @param r1 long long
* @param m1 long long
* @param r2 long long
* @param m2 long long
* @note r1 = r2 = m1 = m2 = -1
*/
void coprimize_simulaneous_congruence_equation(long long& r1, long long& m1, long long& r2, long long& m2) {
long long g = std::gcd(m1, m2);
if((r2 - r1) % g != 0) {
r1 = r2 = m1 = m2 = -1;
return;
}
m1 /= g, m2 /= g;
long long gi = std::gcd(g, m1);
long long gj = g / gi;
do {
g = std::gcd(gi, gj);
gi *= g, gj /= g;
} while(g != 1);
m1 *= gi, m2 *= gj;
r1 %= m1, r2 %= m2;
}
/**
* @brief
* @param r vector<long long>
* @param m vector<long long> mod
* @return std::pair<long long, long long> (, LCM) {-1, -1}
*/
std::pair<long long, long long> crt(const std::vector<long long>& r, const std::vector<long long>& m) {
assert(r.size() == m.size());
if(r.size() == 0) return {0, 1};
int n = (int)r.size();
long long m_lcm = m[0];
long long ans = r[0] % m[0];
for (int i = 1; i < n; i++) {
long long rr = r[i] % m[i], mm = m[i];
coprimize_simulaneous_congruence_equation(ans, m_lcm, rr, mm);
if(m_lcm == -1) return {-1, -1};
long long t = ((rr - ans) * modinv(m_lcm, mm)) % mm;
if(t < 0) t += mm;
ans += t * m_lcm;
m_lcm *= mm;
}
return {ans, m_lcm};
}
/**
* @brief % MOD
* @param r vector<long long>
* @param m vector<long long> mod
* @param MOD long long
* @return std::pair<long long, long long> ( % MOD, LCM % MOD) {-1, -1}
*/
std::pair<long long, long long> crt(const std::vector<long long>& r, const std::vector<long long>& m, long long MOD) {
assert(r.size() == m.size());
if(r.size() == 0) return {0, 1};
int n = (int)r.size();
std::vector<long long> r2 = r, m2 = m;
// m
for(int i = 1; i < n; i++) {
for(int j = 0; j < i; j++) {
coprimize_simulaneous_congruence_equation(r2[i], m2[i], r2[j], m2[j]);
if(m2[i] == -1) return {-1, -1};
}
}
m2.push_back(MOD);
std::vector<long long> prod(n+1, 1); // m2[0] * ... * m2[i - 1] mod m2[i]
std::vector<long long> x(n+1, 0); // i mod m2[i]
for(int i = 0; i < n; i++) {
long long t = (r2[i] - x[i]) * modinv(prod[i], m2[i]) % m2[i];
if(t < 0) t += m2[i];
for(int j = i + 1; j <= n; j++) {
(x[j] += t * prod[j]) %= m2[j];
(prod[j] *= m2[i]) %= m2[j];
}
}
return {x[n], prod[n]};
}
/**
* @brief
*/
namespace NTT {
/**
* @brief
* @param MOD int
* @return int
*/
int calc_primitive_root(int MOD) {
if (MOD == 2) return 1;
if (MOD == 167772161) return 3;
if (MOD == 469762049) return 3;
if (MOD == 754974721) return 11;
if (MOD == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (MOD - 1) >> 1;
while (x % 2 == 0) x >>= 1;
for (long long i = 3; i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt ++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2;; ++ g) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (modpow(g, (MOD - 1) / divs[i], MOD) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
/**
* @brief 2
*/
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return std::max(size_a, size_b) << 1;
}
/**
* @brief NTT
*/
template<class mint> void trans(std::vector<mint>& v, bool inv = false) {
if (v.empty()) return;
int N = (int) v.size();
int MOD = v[0].mod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static std::vector<long long> vbw(30), vibw(30);
if (first) {
first = false;
for (int k = 0; k < 30; ++ k) {
vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
vibw[k] = modinv(vbw[k], MOD);
}
}
for (int i = 0, j = 1; j < N - 1; ++ j) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (i > j) std::swap(v[i], v[j]);
}
for (int k = 0, t = 2; t <= N; ++ k, t <<= 1) {
long long bw = vbw[k];
if (inv) bw = vibw[k];
for (int i = 0; i < N; i += t) {
mint w = 1;
for (int j = 0; j < (t >> 1); ++ j) {
int j1 = i + j, j2 = i + j + (t >> 1);
mint c1 = v[j1], c2 = v[j2] * w;
v[j1] = c1 + c2;
v[j2] = c1 - c2;
w *= bw;
}
}
}
if (inv) {
long long invN = modinv(N, MOD);
for (int i = 0; i < N; ++ i) v[i] = v[i] * invN;
}
}
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = static_modint<MOD0>;
using mint1 = static_modint<MOD1>;
using mint2 = static_modint<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
/**
* @brief
* @param T mint, long long
* @param A vector<T>
* @param B vector<T>
* @return vector<T>
*/
template<class T> std::vector<T> naive
(const std::vector<T>& A, const std::vector<T>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
std::vector<T> res(N + M - 1);
for (int i = 0; i < N; ++ i)
for (int j = 0; j < M; ++ j)
res[i + j] += A[i] * B[j];
return res;
}
};
/**
* @brief modint
* @param A vector<mint>
* @param B vector<mint>
* @return vector<mint>
*/
template<class mint> std::vector<mint> convolution
(const std::vector<mint>& A, const std::vector<mint>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
if (std::min(N, M) < 30) return NTT::naive(A, B);
int MOD = A[0].mod();
int size_fft = NTT::get_fft_size(N, M);
if (MOD == 998244353) {
std::vector<mint> a(size_fft), b(size_fft), c(size_fft);
for (int i = 0; i < N; ++i) a[i] = A[i];
for (int i = 0; i < M; ++i) b[i] = B[i];
NTT::trans(a), NTT::trans(b);
std::vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
NTT::trans(res, true);
res.resize(N + M - 1);
return res;
}
std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++ i) {
a0[i] = A[i].value();
a1[i] = A[i].value();
a2[i] = A[i].value();
}
for (int i = 0; i < M; ++ i) {
b0[i] = B[i].value();
b1[i] = B[i].value();
b2[i] = B[i].value();
}
NTT::trans(a0), NTT::trans(a1), NTT::trans(a2),
NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
static const mint mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
std::vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++ i) {
int y0 = c0[i].value();
int y1 = (NTT::imod0 * (c1[i] - y0)).value();
int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
/**
* @brief long long
* @param A vector<long long>
* @param B vector<long long>
* @return vector<long long>
*/
std::vector<long long> convolution_ll
(const std::vector<long long>& A, const std::vector<long long>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
if (std::min(N, M) < 30) return NTT::naive(A, B);
int size_fft = NTT::get_fft_size(N, M);
std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++ i) {
a0[i] = A[i];
a1[i] = A[i];
a2[i] = A[i];
}
for (int i = 0; i < M; ++ i) {
b0[i] = B[i];
b1[i] = B[i];
b2[i] = B[i];
}
NTT::trans(a0), NTT::trans(a1), NTT::trans(a2),
NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
for (int i = 0; i < size_fft; ++ i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
static const long long mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
static const __int128_t mod012 = (__int128_t)mod01 * NTT::MOD2;
std::vector<long long> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++ i) {
int y0 = c0[i].value();
int y1 = (NTT::imod0 * (c1[i] - y0)).value();
int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
__int128_t tmp = (__int128_t)mod01 * y2 + (__int128_t)mod0 * y1 + y0;
if(tmp < (mod012 >> 1)) res[i] = tmp;
else res[i] = tmp - mod012;
}
return res;
}
#line 5 "cpp/combinatorics.hpp"
/**
* @brief
*/
template <typename Modint>
class Combination {
static std::vector<Modint> fact, inv_fact;
public:
/**
* @brief n
* @param n
* @note O(n) n
*/
inline static void extend(int n) {
int m = fact.size();
if (n < m) return;
fact.resize(n + 1);
inv_fact.resize(n + 1);
for (int i = m; i <= n; ++i) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n] = fact[n].inv();
for (int i = n; i > m; --i) {
inv_fact[i - 1] = inv_fact[i] * i;
}
}
/**
* @brief n
* @param n
* @return n!
* @note extend(n), O(1)
*/
inline static Modint factorial(int n) {
extend(n);
return fact[n];
}
/**
* @brief n
* @param n
* @return n!^-1
* @note extend(n), O(1)
*/
inline static Modint inverse_factorial(int n) {
extend(n);
return inv_fact[n];
}
/**
* @brief n
* @param n
* @return n^-1
* @note extend(n), O(1)
*/
inline static Modint inverse(int n) {
extend(n);
return inv_fact[n] * fact[n - 1];
}
/**
* @brief nPr
* @param n
* @param r
* @return nPr
* @note extend(n), O(1)
*/
inline static Modint P(int n, int r) {
if (r < 0 || n < r) return 0;
extend(n);
return fact[n] * inv_fact[n - r];
}
/**
* @brief nCr
* @param n
* @param r
* @return nCr
* @note extend(n), O(1)
*/
inline static Modint C(int n, int r) {
if (r < 0 || n < r) return 0;
extend(n);
return fact[n] * inv_fact[r] * inv_fact[n - r];
}
/**
* @brief nHr
* @param n
* @param r
* @return nHr
* @note extend(n+r-1), O(1)
*/
inline static Modint H(int n, int r) {
if (n < 0 || r < 0) return 0;
if (n == 0 && r == 0) return 1;
return C(n + r - 1, r);
}
/**
* @brief nPr
* @param n
* @param r
* @return nPr
* @note O(r)
*/
inline static Modint P_loop(long long n, int r) {
if (r < 0 || n < r) return 0;
Modint res = 1;
for (int i = 0; i < r; ++i) {
res *= n - i;
}
return res;
}
/**
* @brief nCr
* @param n
* @param r
* @return nCr
* @note O(min(r, n-r))
*/
inline static Modint C_loop(long long n, long long r) {
if (r < 0 || n < r) return 0;
if(r > n - r) r = n - r;
extend(r);
return P_loop(n, r) * inv_fact[r];
}
/**
* @brief nHr
* @param n
* @param r
* @return nHr
* @note O(r)
*/
inline static Modint H_loop(long long n, long long r) {
if (n < 0 || r < 0) return 0;
if (n == 0 && r == 0) return 1;
return C_loop(n + r - 1, r);
}
/**
* @brief nCr Lucas
* @param n
* @param r
* @return nCr
* @note expand(Mod), O(log(r))
*/
inline static Modint C_lucas(long long n, long long r) {
if (r < 0 || n < r) return 0;
if (r == 0 || n == r) return 1;
Modint res = 1;
while(r > 0) {
int ni = n % Modint::mod(), ri = r % Modint::mod();
if (ni < ri) return 0;
res *= C(ni, ri);
n /= Modint::mod();
r /= Modint::mod();
}
return res;
}
};
template <typename Modint>
std::vector<Modint> Combination<Modint>::fact{1, 1};
template <typename Modint>
std::vector<Modint> Combination<Modint>::inv_fact{1, 1};
struct CombinationPQ {
int p, q;
int pq;
std::vector<int> fact_p, inv_fact_p;
int delta;
CombinationPQ(int p, int q) : p(p), q(q) {
pq = 1;
for(int i = 0; i < q; i++) pq *= p;
fact_p.resize(pq);
fact_p[0] = 1;
for(int i = 1; i < pq; i++) {
if(i % p == 0) fact_p[i] = fact_p[i - 1];
else fact_p[i] = (long long)fact_p[i - 1] * i % pq;
}
inv_fact_p.resize(pq);
inv_fact_p[pq - 1] = modinv(fact_p[pq - 1], pq);
for(int i = pq - 1; i > 0; i--) {
if(i % p == 0) inv_fact_p[i - 1] = inv_fact_p[i];
else inv_fact_p[i - 1] = (long long)inv_fact_p[i] * i % pq;
}
if(p == 2 && q >= 3) delta = 1;
else delta = -1;
}
int C(long long n, long long r) {
if(r < 0 || n < r) return 0;
long long m = n - r;
int ans = 1;
std::vector<int> epsilon;
while(n > 0) {
ans = (long long)ans * fact_p[n % pq] % pq;
ans = (long long)ans * inv_fact_p[m % pq] % pq;
ans = (long long)ans * inv_fact_p[r % pq] % pq;
n /= p;
m /= p;
r /= p;
epsilon.push_back(n - m - r);
}
if(delta == -1 && epsilon.size() >= q && accumulate(epsilon.begin()+q-1, epsilon.end(), 0) % 2 == 1) ans = pq - ans;
if(ans == pq) ans = 0;
int e = accumulate(epsilon.begin(), epsilon.end(), 0);
if(e >= q) ans = 0;
else {
for(int i = 0; i < e; i++) {
ans = (long long)ans * p % pq;
}
}
return ans;
}
};
#line 5 "test/yukicoder-117.test.cpp"
#line 7 "test/yukicoder-117.test.cpp"
int main() {
int t; std::cin >> t;
using C = Combination<modint1000000007>;
while(t--) {
std::string s; std::cin >> s;
s.pop_back();
int i = 2;
while(isdigit(s[i])) ++i;
int n = std::stoi(s.substr(2, i - 2));
int m = std::stoi(s.substr(i+1));
if(s[0] == 'C') {
std::cout << C::C(n, m) << std::endl;
} else if(s[0] == 'P') {
std::cout << C::P(n, m) << std::endl;
} else {
std::cout << C::H(n, m) << std::endl;
}
}
}
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