// This is free and unencumbered software released into the public domain. // Anyone is free to copy, modify, publish, use, compile, sell, or // distribute this software, either in source code form or as a compiled // binary, for any purpose, commercial or non-commercial, and by any // means. // In jurisdictions that recognize copyright laws, the author or authors // of this software dedicate any and all copyright interest in the // software to the public domain. We make this dedication for the benefit // of the public at large and to the detriment of our heirs and // successors. We intend this dedication to be an overt act of // relinquishment in perpetuity of all present and future rights to this // software under copyright law. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF // MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. // IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR // OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, // ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR // OTHER DEALINGS IN THE SOFTWARE. // For more information, please refer to /****************/ /* template.hpp */ /****************/ #include #include #include #include #include #include using std::cerr; using std::cout; using std::endl; using std::max; using std::min; using std::swap; struct BoolName : std::numpunct { std::string t, f; BoolName(std::string t, std::string f) : t(t), f(f) {} std::string do_truename() const { return t; } std::string do_falsename() const { return f; } }; void setBoolName(std::string t, std::string f) { cout.imbue(std::locale(cout.getloc(), new BoolName(t, f))); } struct Initializer { Initializer() { cout << std::fixed << std::setprecision(15) << std::boolalpha; setBoolName("Yes", "No"); } } initializer; struct Input { bool eof; Input() : eof(false) {} operator char() { char v; while (!(this->eof = (std::scanf("%c", &v) != 1)) && std::isspace(v)) { } return v; } operator int() { int v; this->eof = (std::scanf("%d", &v) != 1); return v; } operator long() { long v; this->eof = (std::scanf("%ld", &v) != 1); return v; } operator long long() { long long v; this->eof = (std::scanf("%lld", &v) != 1); return v; } operator unsigned int() { unsigned int v; this->eof = (std::scanf("%u", &v) != 1); return v; } operator unsigned long() { unsigned long v; this->eof = (std::scanf("%lu", &v) != 1); return v; } operator unsigned long long() { unsigned long long v; this->eof = (std::scanf("%llu", &v) != 1); return v; } operator double() { double v; this->eof = (std::scanf("%lf", &v) != 1); return v; } operator long double() { long double v; this->eof = (std::scanf("%Lf", &v) != 1); return v; } void ignore() const { getchar(); } } in; template T abs(T a) { return a >= 0 ? a : -a; } template bool chmin(T &a, const S &b) { return a > b ? a = b, true : false; } template bool chmax(T &a, const S &b) { return a < b ? a = b, true : false; } template std::function cast() { return [](const T &t) { return static_cast(t); }; } template T copy(const T &a) { return T(a); } class ZeroPadding { public: ZeroPadding(int n) : n(n) {} int n; }; std::ostream &operator<<(std::ostream &os, const ZeroPadding &z) { os << std::setw(z.n) << std::setfill('0'); return os; } template constexpr T inf() { return std::numeric_limits::max() / 2 - 1; } /*********************/ /* bit_operation.hpp */ /*********************/ template int least_bit(T n) { static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size"); if (sizeof(T) == 4) { return __builtin_ffs(n) - 1; } if (sizeof(T) == 8) { return __builtin_ffsll(n) - 1; } } // n must be greater than 0. template int least_bit_fast(T n) { static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size"); if (sizeof(T) == 4) { return __builtin_ctz(n); } if (sizeof(T) == 8) { return __builtin_ctzll(n); } } template int most_bit(T n) { static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size"); if (sizeof(T) == 4) { return n ? 31 - __builtin_clz(n) : -1; } if (sizeof(T) == 8) { return n ? 63 - __builtin_clzll(n) : -1; } } template int count_bit(T n) { static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size"); if (sizeof(T) == 4) { return __builtin_popcount(n); } if (sizeof(T) == 8) { return __builtin_popcountll(n); } } template int bit_parity(T n) { static_assert(sizeof(T) == 4 || sizeof(T) == 8, "unsupported size"); if (sizeof(T) == 4) { return __builtin_parity(n); } if (sizeof(T) == 8) { return __builtin_parityll(n); } } /*************/ /* tuple.hpp */ /*************/ #include template class Tuple : public std::tuple { public: Tuple(Input &in) : std::tuple() { (void)in; } }; template class Tuple : public std::tuple { public: Tuple() : std::tuple() {} Tuple(T t, S... s) : std::tuple(t, s...) {} Tuple(const std::tuple &t) : std::tuple(t) {} Tuple(Input &in) { auto a = std::tuple(in); std::tuple b = Tuple(in); std::tuple c = std::tuple_cat(a, b); *this = c; } template auto &get() { return std::get(*this); } template const auto &get() const { return std::get(*this); } }; template Tuple makeTuple(const T &... args) { return Tuple(args...); } namespace std { template class tuple_size> : public std::integral_constant {}; template class tuple_element> { public: using type = tuple_element_t>; }; } // namespace std /*****************/ /* container.hpp */ /*****************/ #include template class Container : public T { private: using S = typename T::value_type; using Itr = typename T::iterator; public: Container() : T() {} Container(int n) : T(n) {} Container(int n, S s) : T(n, s) {} template Container(Itr first, Itr last) : T(first, last) {} Container(const std::initializer_list &v) : T(v) {} Container(int n, Input &in) { std::vector v(n); for (auto &i : v) { i = in; } *this = Container(v.begin(), v.end()); } S max() const { return *std::max_element(this->begin(), this->end()); } template auto max(Function func) const { std::vector> res; for (const auto &i : *this) { res.emplace_back(func(i), i); } return std::max_element(res.begin(), res.end())->second; } S min() const { return *std::min_element(this->begin(), this->end()); } Tuple minmax() const { auto itrs = std::minmax_element(this->begin(), this->end()); return Tuple(*itrs.first, *itrs.second); } template auto min(Function func) const { std::vector> res; for (const auto &i : *this) { res.emplace_back(func(i), i); } return std::min_element(res.begin(), res.end())->second; } int argmax() const { return std::distance(this->begin(), std::max_element(this->begin(), this->end())); } int argmin() const { return std::distance(this->begin(), std::min_element(this->begin(), this->end())); } int find(const S &a) const { return std::distance(this->begin(), std::find(this->begin(), this->end(), a)); } bool contains(const S &a) const { return std::find(this->begin(), this->end(), a) != this->end(); } int size() const { return T::size(); } std::pair equal_range(const S &a) { return std::equal_range(this->begin(), this->end(), a); } template bool all_of(Function func) const { return std::all_of(this->begin(), this->end(), func); } template bool any_of(Function func) const { return std::any_of(this->begin(), this->end(), func); } template bool none_of(Function func) const { return std::none_of(this->begin(), this->end(), func); } int count(const S &s) const { return std::count(this->begin(), this->end(), s); } bool is_sorted() const { return std::is_sorted(this->begin(), this->end()); } void output(std::string sep = "\n", std::string end = "\n") const { bool first = true; for (const auto &i : *this) { if (!first) { cout << sep; } first = false; cout << i; } cout << end; } }; /***********/ /* map.hpp */ /***********/ #include template class Map : public Container> { public: Map() : Container>() {} bool contains(const T &a) const { return this->count(a) != 0; } int count(const T &t) const { return std::map::count(t); } }; /***************/ /* ordered.hpp */ /***************/ template class Ordered { public: template bool operator==(const V &v) const { return !(static_cast(v) < static_cast(*this) || static_cast(*this) < static_cast(v)); } template bool operator!=(const V &v) const { return static_cast(v) < static_cast(*this) || static_cast(*this) < static_cast(v); } template bool operator>(const V &v) const { return static_cast(v) < static_cast(*this); } template bool operator<=(const V &v) const { return !(static_cast(v) < static_cast(*this)); } template bool operator>=(const V &v) const { return !(static_cast(*this) < static_cast(v)); } }; /**************/ /* vector.hpp */ /**************/ #include template class Vector : public Container>, public Ordered> { public: Vector() = default; Vector(const Vector &v) = default; Vector(int n) : Container>(n) {} Vector(int n, T t) : Container>(n, t) {} template Vector(Itr first, Itr last) : Container>(first, last) {} Vector(const std::initializer_list &v) : Container>(v) {} Vector(int n, Input &in) : Container>(n, in) {} Vector &operator+=(const Vector &v) { if (this->size() < v.size()) { this->resize(v.size()); } for (int i = 0; i < v.size(); ++i) { (*this)[i] += v[i]; } return *this; } Vector &operator+=(const T &v) { for (auto &i : *this) { i += v; } return *this; } Vector &operator-=(const Vector &v) { if (this->size() < v.size()) { this->resize(v.size()); } for (int i = 0; i < v.size(); ++i) { (*this)[i] -= v[i]; } return *this; } Vector &operator-=(const T &v) { for (auto &i : *this) { i -= v; } return *this; } Vector &operator*=(const Vector &v) { for (int i = 0; i < this->size(); ++i) { (*this)[i] *= v[i]; } return *this; } Vector &operator*=(const T &v) { for (auto &i : *this) { i *= v; } return *this; } Vector &operator/=(const Vector &v) { for (int i = 0; i < this->size(); ++i) { (*this)[i] /= v[i]; } return *this; } Vector &operator/=(const T &v) { for (auto &i : *this) { i /= v; } return *this; } Vector &operator%=(const Vector &v) { for (int i = 0; i < this->size(); ++i) { (*this)[i] %= v[i]; } return *this; } Vector &operator%=(const T &v) { for (auto &i : *this) { i %= v; } return *this; } Vector operator+(const Vector &v) const { return Vector(*this) += v; } Vector operator+(const T &v) const { return Vector(*this) += v; } Vector operator-(const Vector &v) const { return Vector(*this) -= v; } Vector operator-(const T &v) const { return Vector(*this) -= v; } Vector operator*(const Vector &v) const { return Vector(*this) *= v; } Vector operator*(const T &v) const { return Vector(*this) *= v; } Vector operator/(const Vector &v) const { return Vector(*this) /= v; } Vector operator/(const T &v) const { return Vector(*this) /= v; } Vector operator%(const Vector &v) const { return Vector(*this) %= v; } Vector operator%(const T &v) const { return Vector(*this) %= v; } bool operator<(const Vector &v) const { if (this->size() != v.size()) { return this->size() < v.size(); } for (int i = 0; i < this->size(); ++i) { if ((*this)[i] != v[i]) { return (*this)[i] < v[i]; } } return false; } Vector operator-() const { return *this * -1; } T inner_product(const Vector &v) const { return std::inner_product(this->begin(), this->end(), v.begin(), T(0)); } Vector &partial_sort(int k, bool reverse = false) { if (!reverse) { std::partial_sort(this->begin(), this->begin() + k, this->end()); } else { std::partial_sort(this->begin(), this->begin() + k, this->end(), std::greater()); } return *this; } Vector &sort() { std::sort(this->begin(), this->end()); return *this; } template Vector &sort(Function func) { std::sort(this->begin(), this->end(), func); return *this; } Vector &rsort() { std::sort(this->rbegin(), this->rend()); return *this; } Vector argsort() const { Vector> v; for (int i = 0; i < this->size(); ++i) { v.emplace_back((*this)[i], i); } v.sort(); auto f = [](const Tuple &t) { return t.template get<1>(); }; return v.transform(f); } Vector &nth_element(int n, bool reverse = false) { if (!reverse) { std::nth_element(this->begin(), this->begin() + n, this->end()); } else { std::nth_element(this->begin(), this->begin() + n, this->end(), std::greater()); } return *this; } Vector subvector(int a) const { return Vector(this->begin(), this->begin() + a); } Vector subvector(int a, int b) const { return Vector(this->begin() + a, this->begin() + b); } template auto transform(Function func) const { Vector res; std::transform(this->begin(), this->end(), std::back_inserter(res), func); return res; } Vector partial_sum() const { Vector res; std::partial_sum(this->begin(), this->end(), std::back_inserter(res)); return res; } template Vector partial_sum(Function func) const { Vector res; std::partial_sum(this->begin(), this->end(), std::back_inserter(res), func); return res; } Vector &reverse() { std::reverse(this->begin(), this->end()); return *this; } template int count_if(Function func) const { return std::count_if(this->begin(), this->end(), func); } Vector adjacent_difference() const { Vector res; std::adjacent_difference(this->begin(), this->end(), std::back_inserter(res)); return res; } T lower_bound(T t) const { return std::lower_bound(this->begin(), this->end(), t) - this->begin(); } T upper_bound(T t) const { return std::upper_bound(this->begin(), this->end(), t) - this->begin(); } T accumulate() const { return std::accumulate(this->begin(), this->end(), T()); } template S accumulate(S n, Function func) const { return std::accumulate(this->begin(), this->end(), n, func); } template static Vector makeVector(Int n) { return Vector(n); } template static Vector makeVector(Input &in, Int n) { return Vector(n, in); } template static auto makeVector(Input &in, Int n, Ints... ints) { Vector res; for (int i = 0; i < n; ++i) { res.emplace_back(makeVector(in, ints...)); } return res; } template static auto makeVector(Int n, Ints... ints) { Vector res; for (int i = 0; i < n; ++i) { res.emplace_back(makeVector(ints...)); } return res; } Vector &unique() { this->erase(std::unique(this->begin(), this->end()), this->end()); return *this; } bool next_permutation() { return std::next_permutation(this->begin(), this->end()); } Vector &rotate(int n) { std::rotate(this->begin(), this->begin() + n, this->end()); return *this; } Map countAll() const { Map res; for (const auto &i : *this) { ++res[i]; } return res; } T matmul(const T &a) const { return this->transform([&](const T &i) { return i.inner_product(a); }); } }; template Vector iota(int n, T m = 0) { Vector v(n); std::iota(v.begin(), v.end(), m); return v; } template void read(Vector &t, Vector &s) { for (int i = 0; i < t.size(); ++i) { t[i] = T(in); s[i] = S(in); } } template void read(Vector &t, Vector &s, Vector &u) { for (int i = 0; i < t.size(); ++i) { t[i] = T(in); s[i] = S(in); u[i] = U(in); } } template Vector operator+(const T &a, const Vector &b) { return b + a; } template Vector operator-(const T &a, const Vector &b) { return -b + a; } template Vector operator*(const T &a, const Vector &b) { return b * a; } /************/ /* math.hpp */ /************/ #include template constexpr T pi() { return acos(T(-1)); } template T gcd(T t) { return abs(t); } template T gcd(T a, S... s) { a = abs(a); auto b = gcd(s...); if (a == 0 || b == 0) { return max(a, b); } int fa = least_bit_fast(a); int fb = least_bit_fast(b); a >>= fa; b >>= fb; while (a != b) { auto &c = a > b ? a : b; c = abs(a - b); c >>= least_bit_fast(c); } return a << min(fa, fb); } template T gcd(const Vector &v) { T g = abs(v[0]); for (int i = 1; i < int(v.size()); ++i) { g = gcd(g, v[i]); } return g; } template T lcm(T t) { return abs(t); } template T lcm(T t, S... s) { T l = lcm(s...); return abs(t) / gcd(t, l) * l; } template T lcm(const Vector &v) { T l = abs(v[0]); for (int i = 1; i < int(v.size()); ++i) { l = lcm(l, v[i]); } return l; } template T floor(T a, T b) { auto d = std::div(a, b); return d.quot - (d.rem && (a < 0) != (b < 0) ? 1 : 0); } template T ceil(T a, T b) { auto d = std::div(a, b); return d.quot + (d.rem && (a > 0) == (b > 0) ? 1 : 0); } template T round(T a) { return std::round(a); } template T round(T a, T b) { return floor(a + b / 2, b); } template T mod(T a, T b) { T c = a % b; return c < 0 ? c + abs(b) : c; } template T factorial(T n) { return n <= 1 ? 1 : factorial(n - 1) * n; } template Vector factorial_vector(int n) { Vector v(n + 1, 1); for (int i = 1; i <= n; ++i) { v[i] = v[i - 1] * i; } return v; } template T square(T n) { return n * n; } template T cube(T n) { return n * n * n; } template T norm(T x1, T y1, T x2, T y2) { return square(x1 - x2) + square(y1 - y2); } template bool isSquare(T n) { return square(T(sqrt(n))) == n; } template T clamp(T v, T l, T u) { return v < l ? l : v > u ? u : v; } template auto hypot(T a, T b) { return std::hypot(a, b); } template auto pow(T a, T b) { return std::pow(a, b); } template auto log10(T a) { return std::log10(a); } template T sqrt_int(T a) { T x = std::sqrt(a); while (x * x > a) { --x; } while ((x + 1) * (x + 1) < a) { ++x; } return x; } /************************/ /* math/combination.hpp */ /************************/ template class Combination { private: Vector factorial; public: Combination(int n = 0) : factorial(n + 1, 1) { for (int i = 1; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } T partial_permutation(int n, int m) { if (n < m) { return 0; } if (n < factorial.size()) { return factorial[n] / factorial[n - m]; } T res = 1; for (int i = n; i > n - m; --i) { res *= i; } return res; } T combination(int n, int m) { if (n < m) { return 0; } if (n < factorial.size()) { return factorial[n] / factorial[m] / factorial[n - m]; } T res = 1; for (int i = 0; i < min(m, n - m); ++i) { res = res * (n - i) / (i + 1); } return res; } T combination_safety(int n, int m) { m = min(m, n - m); auto a = iota(m, n - m + 1), b = iota(m, 1); for (auto i : b) { for (auto &j : a) { auto g = gcd(i, j); i /= g; j /= g; if (i == 1) { break; } } } return a.accumulate(T(1), std::multiplies()); } T repetition(int n, int m) { if (m == 0) { return 1; } return combination(n + m - 1, m); } }; /******************/ /* arithmetic.hpp */ /******************/ template class Addition { public: template T operator+(const V &v) const { return T(static_cast(*this)) += v; } T operator++() { return static_cast(*this) += 1; } }; template class Subtraction { public: template T operator-(const V &v) const { return T(static_cast(*this)) -= v; } }; template class Multiplication { public: template T operator*(const V &v) const { return T(static_cast(*this)) *= v; } }; template class Division { public: template T operator/(const V &v) const { return T(static_cast(*this)) /= v; } }; template class Modulus { public: template T operator%(const V &v) const { return T(static_cast(*this)) %= v; } }; template class IndivisibleArithmetic : public Addition, public Subtraction, public Multiplication {}; template class Arithmetic : public IndivisibleArithmetic, public Division {}; /********************/ /* math/inverse.hpp */ /********************/ class Inverse { private: int64_t mod; Vector inv; public: Inverse() {} Inverse(int64_t mod, int64_t n = 1000000) : mod(mod), inv(n, 1) { for (int i = 2; i < n; ++i) { inv[i] = inv[mod % i] * (mod - mod / i) % mod; } } int64_t operator()(int64_t a) const { if (a < inv.size()) { return inv[a]; } int64_t b = mod, x = 1, y = 0; while (b) { int64_t t = a / b; swap(a -= t * b, b); swap(x -= t * y, y); } return x < 0 ? x + mod : x; } }; int64_t inverse(int64_t n, int64_t mod) { Inverse inv(mod, 0); return inv(n); } /*****************/ /* math/mint.hpp */ /*****************/ class Mint : public Arithmetic { private: static int64_t mod; static Inverse inverse; int64_t val; public: Mint() : val(0) {} Mint(const int64_t &val) { this->val = val % mod; if (this->val < 0) { this->val += mod; } } Mint(Input &in) : val(in) { this->val = this->val % mod; if (this->val < 0) { this->val += mod; } } static void setMod(const int64_t &m) { mod = m; inverse = Inverse(m); } Mint operator-() const { return Mint(val ? mod - val : 0); } Mint &operator+=(const Mint &m) { val += m.val; if (val >= mod) { val -= mod; } return *this; } Mint &operator-=(const Mint &m) { val -= m.val; if (val < 0) { val += mod; } return *this; } Mint &operator*=(const Mint &m) { val *= m.val; val %= mod; return *this; } Mint &operator/=(const Mint &m) { val *= inverse(m.val); val %= mod; return *this; } bool operator==(const Mint &m) const { return val == m.val; } Mint &operator++() { return *this += 1; } Mint &operator--() { return *this -= 1; } template Mint operator-(const T &m) { return Arithmetic::operator-(m); } explicit operator char() const { return val; } explicit operator int() const { return val; } explicit operator int64_t() const { return val; } static Mint identity() { return 1; } }; int64_t Mint::mod = 1000000007; Inverse Mint::inverse(1000000007); std::ostream &operator<<(std::ostream &os, Mint a) { os << int64_t(a); return os; } Mint operator+(const int &n, const Mint &m) { return m + n; } Mint operator-(const int &n, const Mint &m) { return -m + n; } Mint operator*(const int &n, const Mint &m) { return m * n; } Mint operator/(const int &n, const Mint &m) { return Mint(n) / m; } Mint operator+(const int64_t &n, const Mint &m) { return m + n; } Mint operator-(const int64_t &n, const Mint &m) { return -m + n; } Mint operator*(const int64_t &n, const Mint &m) { return m * n; } Mint operator/(const int64_t &n, const Mint &m) { return Mint(n) / m; } /************/ /* main.cpp */ /************/ int main() { int64_t n(in), m(in); n /= 1000; n %= m; Mint::setMod(1000000000); Combination comb; cout << comb.combination_safety(m, n) << endl; }