結果
問題 | No.117 組み合わせの数 |
ユーザー |
![]() |
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 (参考情報) |
judge4 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 1 |
ソースコード
#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 四則演算において自動で mod を取るクラス*/#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ビット符号なし整数の素数判定// 参考: M. Forisek and J. Jancina, “Fast Primality Testing for Integers That Fit into a Machine Word,” presented at the Conference on CurrentTrends 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 と dynamic_modint の実装を CRTP によって行うためのクラステンプレート/// @tparam Modint このクラステンプレートを継承するクラスtemplate <class Modint>class modint_base {public:/// @brief 保持する値の型using value_type = std::uint32_t;/// @brief 0 で初期化します。constexpr modint_base() noexcept: m_value{ 0 } {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値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 の剰余で初期化します。/// @param value 初期化に使う値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 保持している値を取得します。/// @return 保持している値[[nodiscard]]constexpr value_type value() const noexcept {return m_value;}/// @brief 保持している値をインクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint& operator++() noexcept {++m_value;if (m_value == Modint::mod()) {m_value = 0;}return static_cast<Modint&>(*this);}/// @brief 保持している値をインクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint operator++(int) noexcept {auto x = static_cast<const Modint&>(*this);++*this;return x;}/// @brief 保持している値をデクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint& operator--() noexcept {if (m_value == 0) {m_value = Modint::mod();}--m_value;return static_cast<Modint&>(*this);}/// @brief 保持している値をデクリメントして、剰余を取ります。/// @return @c *thisconstexpr Modint operator--(int) noexcept {auto x = static_cast<const Modint&>(*this);--*this;return x;}/// @brief 保持している値に @c x の持つ値を足して、剰余を取ります。/// @param x 足す数/// @return @c *thisconstexpr 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 保持している値から @c x の持つ値を引いて、剰余を取ります。/// @param x 引く数/// @return @c *thisconstexpr 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 保持している値に @c x の持つ値を掛けて、剰余を取ります。/// @param x 掛ける数/// @return @c *thisconstexpr 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 保持している値を @c x の持つ値で割って、剰余を取ります。/// @remark 時間計算量: @f$O(\log x)@f$/// @param x 割る数/// @return @c *thisconstexpr Modint& operator/=(const Modint& x) noexcept {return *this *= x.inv();}/// @brief 自身のコピーを返します。/// @return @c *this[[nodiscard]]constexpr Modint operator+() const noexcept {return static_cast<const Modint&>(*this);}/// @brief 自身の反数を返します。/// @return 自身の反数[[nodiscard]]constexpr Modint operator-() const noexcept {return 0 - static_cast<const Modint&>(*this);}/// @brief 自身の @c n 乗を返します。/// @remark 時間計算量: @f$O(\log n)@f$/// @param n 指数/// @return 自身の @c n 乗[[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 自身の逆数を返します。/// @remark 時間計算量: @f$O(\log value)@f$/// @return 自身の逆数[[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 に @c y を足したオブジェクトを返します。/// @param x 足される数/// @param y 足す数/// @return @c x に @c y を足したオブジェクト[[nodiscard]]friend constexpr Modint operator+(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } += y);}/// @brief @c x から @c y を引いたオブジェクトを返します。/// @param x 引かれる数/// @param y 引く数/// @return @c x から @c y を引いたオブジェクト[[nodiscard]]friend constexpr Modint operator-(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } -= y);}/// @brief @c x に @c y を掛けたオブジェクトを返します。/// @param x 掛けられる数/// @param y 掛ける数/// @return @c x に @c y を掛けたオブジェクト[[nodiscard]]friend constexpr Modint operator*(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } *= y);}/// @brief @c x を @c y で割ったオブジェクトを返します。/// @param x 割られる数/// @param y 割る数/// @return @c x を @c y で割ったオブジェクト[[nodiscard]]friend constexpr Modint operator/(const Modint& x, const Modint& y) noexcept {return std::move(Modint{ x } /= y);}/// @brief @c x と @c y の保持する値が等しいかどうかを調べます。/// @return @c x と @c y の保持する値が等しければ @c true 、そうでなければ @c false[[nodiscard]]friend constexpr bool operator==(const Modint& x, const Modint& y) noexcept {return x.m_value == y.m_value;}/// @brief @c x と @c y の保持する値が等しくないかどうかを調べます。/// @return @c x と @c y の保持する値が等しければ @c false 、そうでなければ @c true[[nodiscard]]friend constexpr bool operator!=(const Modint& x, const Modint& y) noexcept {return not (x == y);}/// @brief 入力ストリームから符号付き整数を読み取り、 @c x に格納します。/// @tparam CharT 入力ストリームの文字型/// @tparam Traits 入力ストリームの文字トレイト/// @param is 入力ストリーム/// @param x 入力を受け取るオブジェクト/// @return @c istemplate <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 出力ストリームに @c x の保持する値を出力します。/// @tparam CharT 出力ストリームの文字型/// @tparam Traits 出力ストリームの文字トレイト/// @param os 出力ストリーム/// @param x 出力するオブジェクト/// @return @c ostemplate <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 コンパイル時に法が決まるとき、四則演算において自動で mod を取るクラス/// @tparam Mod 法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 法を取得します。/// @return 法[[nodiscard]]static constexpr value_type mod() noexcept {return Mod;}/// @brief 0 で初期化します。constexpr static_modint() noexcept: base_type{} {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>constexpr static_modint(SignedIntegral value) noexcept: base_type{value} {}/// @brief 自身の逆数を返します。/// @remark 時間計算量: @f$O(\log value)@f$/// @return 自身の逆数[[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 実行時に法が決まるとき、四則演算において自動で mod を取るクラス/// @tparam ID このIDごとに法を設定することができます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 法を取得します。/// @return 法[[nodiscard]]static value_type mod() noexcept {return modulus;}/// @brief 法を設定します。/// @param m 新しい法static void set_mod(value_type m) noexcept {assert(m > 0 && m <= std::numeric_limits<value_type>::max() / 2);modulus = m;}/// @brief 0 で初期化します。constexpr dynamic_modint() noexcept: base_type{} {}/// @brief @c value の剰余で初期化します。/// @param value 初期化に使う値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を返す* @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を返す* @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 2式の連立合同式を、mが互いに素になるように変形する* @param r1 long long* @param m1 long long* @param r2 long long* @param m2 long long* @note 矛盾する場合、r1 = r2 = m1 = m2 = -1となる*/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 連立合同式を解く* @param r vector<long long> 余りの配列* @param m vector<long long> modの配列* @return std::pair<long long, long long> (解, LCM) 解なしのときは{-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 連立合同式の最小の非負整数解 % MODを求める* @param r vector<long long> 余りの配列* @param m vector<long long> modの配列* @param MOD long long* @return std::pair<long long, long long> (最小解 % MOD, LCM % MOD) 解なしのときは{-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を互いに素にする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番目までの解 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 畳み込み*/namespace NTT {/*** @brief 原子根* @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 畳み込みのサイズを2のべき乗にする*/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 配列のサイズが小さいときの畳み込み* @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の畳み込み* @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の畳み込み* @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 組み合わせ*/template <typename Modint>class Combination {static std::vector<Modint> fact, inv_fact;public:/*** @brief n までの階乗とその逆元を前計算する* @param n* @note O(n) 必要になったら呼び出されるが、予め大きなnに対して呼び出しておくことで逆元の直接計算を減らせる*/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 の階乗を返す* @param n* @return n!* @note extend(n), O(1)*/inline static Modint factorial(int n) {extend(n);return fact[n];}/*** @brief n の階乗の逆元を返す* @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 の逆元を返す* @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 を返す* @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 を返す* @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 を返す* @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 を定義どおり計算する* @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 を定義どおり計算する* @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 を定義どおり計算する* @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 を Lucas の定理を用いて計算する* @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;}}}