#line 1 "main.cpp" #include #line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp" #line 6 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp" #include #ifdef _MSC_VER #include #endif #line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp" #line 5 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp" #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(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 (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp" #line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp" namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder #line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp" namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime; }; template struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder #line 1 "/home/anqooqie/.proconlib/tools/fact_mod_cache.hpp" #line 1 "/home/anqooqie/.proconlib/tools/is_prime.hpp" #line 1 "/home/anqooqie/.proconlib/tools/prod_mod.hpp" namespace tools { template constexpr T3 prod_mod(const T1 x, const T2 y, const T3 m) { using u128 = unsigned __int128; u128 prod_mod = u128(x >= 0 ? x : -x) * u128(y >= 0 ? y : -y) % u128(m); if ((x >= 0) ^ (y >= 0)) prod_mod = u128(m) - prod_mod; return prod_mod; } } #line 1 "/home/anqooqie/.proconlib/tools/pow_mod.hpp" #line 1 "/home/anqooqie/.proconlib/tools/mod.hpp" #line 1 "/home/anqooqie/.proconlib/tools/quo.hpp" #line 5 "/home/anqooqie/.proconlib/tools/quo.hpp" namespace tools { template constexpr ::std::common_type_t quo(const M lhs, const N rhs) { if (lhs >= 0) { return lhs / rhs; } else { if (rhs >= 0) { return -((-lhs - 1 + rhs) / rhs); } else { return (-lhs - 1 + -rhs) / -rhs; } } } } #line 6 "/home/anqooqie/.proconlib/tools/mod.hpp" namespace tools { template constexpr ::std::common_type_t mod(const M lhs, const N rhs) { if constexpr (::std::is_unsigned_v && ::std::is_unsigned_v) { return lhs % rhs; } else { return lhs - ::tools::quo(lhs, rhs) * rhs; } } } #line 6 "/home/anqooqie/.proconlib/tools/pow_mod.hpp" namespace tools { template constexpr T3 pow_mod(const T1 x, T2 n, const T3 m) { if (m == 1) return 0; T3 r = 1; T3 y = ::tools::mod(x, m); while (n > 0) { if ((n & 1) > 0) { r = ::tools::prod_mod(r, y, m); } y = ::tools::prod_mod(y, y, m); n /= 2; } return r; } } #line 7 "/home/anqooqie/.proconlib/tools/is_prime.hpp" namespace tools { constexpr bool is_prime(const ::std::uint_fast64_t n) { constexpr ::std::array bases = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; if (n <= 1) return false; if (n == 2) return true; if (n % 2 == 0) return false; auto d = n - 1; for (; d % 2 == 0; d /= 2); for (const auto a : bases) { if (a % n == 0) return true; auto power = d; auto target = ::tools::pow_mod(a, power, n); bool is_composite = true; if (target == 1) is_composite = false; for (; is_composite && power != n - 1; power *= 2, target = ::tools::prod_mod(target, target, n)) { if (target == n - 1) is_composite = false; } if (is_composite) { return false; } } return true; } } #line 1 "/home/anqooqie/.proconlib/tools/ssize.hpp" #line 6 "/home/anqooqie/.proconlib/tools/ssize.hpp" namespace tools { template constexpr auto ssize(const C& c) -> ::std::common_type_t<::std::ptrdiff_t, ::std::make_signed_t> { return c.size(); } } #line 10 "/home/anqooqie/.proconlib/tools/fact_mod_cache.hpp" namespace tools { template class fact_mod_cache { private: ::std::vector m_inv; ::std::vector m_fact; ::std::vector m_fact_inv; public: fact_mod_cache() : m_inv({M::raw(0), M::raw(1)}), m_fact({M::raw(1), M::raw(1)}), m_fact_inv({M::raw(1), M::raw(1)}) { assert(::tools::is_prime(M::mod())); } fact_mod_cache(const ::tools::fact_mod_cache&) = default; fact_mod_cache(::tools::fact_mod_cache&&) = default; ~fact_mod_cache() = default; ::tools::fact_mod_cache& operator=(const ::tools::fact_mod_cache&) = default; ::tools::fact_mod_cache& operator=(::tools::fact_mod_cache&&) = default; M inv(const long long n) { assert(n % M::mod() != 0); const long long size = ::tools::ssize(this->m_inv); this->m_inv.resize(::std::clamp(::std::abs(n) + 1, size, M::mod())); for (long long i = size; i < ::tools::ssize(this->m_inv); ++i) { this->m_inv[i] = -this->m_inv[M::mod() % i] * M::raw(M::mod() / i); } M result = this->m_inv[::std::abs(n) % M::mod()]; if (n < 0) result = -result; return result; } M fact(const long long n) { assert(n >= 0); const long long size = ::tools::ssize(this->m_fact); this->m_fact.resize(::std::clamp(n + 1, size, M::mod())); for (long long i = size; i < ::tools::ssize(this->m_fact); ++i) { this->m_fact[i] = this->m_fact[i - 1] * M::raw(i); } return n < M::mod() ? this->m_fact[n] : M::raw(0); } M fact_inv(const long long n) { assert(0 <= n && n < M::mod()); const long long size = ::tools::ssize(this->m_fact_inv); this->m_fact_inv.resize(::std::max(size, n + 1)); this->inv(this->m_fact_inv.size() - 1); for (long long i = size; i < ::tools::ssize(this->m_fact_inv); ++i) { this->m_fact_inv[i] = this->m_fact_inv[i - 1] * this->m_inv[i]; } return this->m_fact_inv[n]; } explicit fact_mod_cache(const long long max) : fact_mod_cache() { this->fact(::std::min(max, M::mod() - 1)); this->fact_inv(::std::min(max, M::mod() - 1)); } M combination(long long n, long long r) { if (!(0 <= r && r <= n)) return M::raw(0); this->fact(::std::min(n, M::mod() - 1)); this->fact_inv(::std::min(n, M::mod() - 1)); const auto c = [&](const long long nn, const long long rr) { return 0 <= rr && rr <= nn ? this->m_fact[nn] * this->m_fact_inv[nn - rr] * this->m_fact_inv[rr] : M::raw(0); }; M result(1); while (n > 0 || r > 0) { result *= c(n % M::mod(), r % M::mod()); n /= M::mod(); r /= M::mod(); } return result; } M permutation(const long long n, const long long r) { if (!(0 <= r && r <= n)) return M::raw(0); return this->combination(n, r) * this->fact(r); } }; } #line 4 "main.cpp" using mint = atcoder::modint1000000007; tools::fact_mod_cache cache; int main() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); int T; std::cin >> T; std::cin.ignore(); for (int t = 0; t < T; ++t) { char type; std::cin >> type; std::cin.ignore(); int N, K; std::cin >> N; std::cin.ignore(); std::cin >> K; std::cin.ignore(); std::cin.ignore(); if (type == 'C') { std::cout << cache.combination(N, K).val() << '\n'; } else if (type == 'P') { std::cout << cache.permutation(N, K).val() << '\n'; } else if (type == 'H') { std::cout << cache.combination(N + K - 1, K).val() << '\n'; } else { std::exit(EXIT_FAILURE); } } return 0; }