結果

問題 No.802 だいたい等差数列
ユーザー yuruhiya
提出日時 2021-04-04 10:13:17
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 20,628 bytes
コンパイル時間 30,160 ms
コンパイル使用メモリ 5,248 KB
最終ジャッジ日時 2025-01-20 11:03:12
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ソースコード

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プレゼンテーションモードにする

#line 2 "/home/yuruhiya/programming/library/Utility/get_MOD.cpp"
constexpr long long get_MOD() {
#ifdef SET_MOD
    return SET_MOD;
#else
    return 1000000007;
#endif
}
#line 3 "/home/yuruhiya/programming/library/Utility/constants.cpp"
#include <vector>
#include <string>
#include <utility>
#include <queue>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define rrep(i, n) for (int i = (n)-1; i >= 0; --i)
#define rfor(i, m, n) for (int i = (m); i >= (n); --i)
#define loop(n) rep(i##__COUNTER__, n)
#define unless(c) if (!(c))
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)
using ll = long long;
using LD = long double;
using VB = std::vector<bool>;
using VVB = std::vector<VB>;
using VI = std::vector<int>;
using VVI = std::vector<VI>;
using VL = std::vector<ll>;
using VVL = std::vector<VL>;
using VS = std::vector<std::string>;
using VD = std::vector<LD>;
using PII = std::pair<int, int>;
using VP = std::vector<PII>;
using PLL = std::pair<ll, ll>;
using VPL = std::vector<PLL>;
template <class T> using PQ = std::priority_queue<T>;
template <class T> using PQS = std::priority_queue<T, std::vector<T>, std::greater<T>>;
constexpr int inf = 1000000000;
constexpr long long inf_ll = 1000000000000000000ll, MOD = get_MOD();
constexpr long double PI = 3.14159265358979323846, EPS = 1e-12;
#line 2 "/home/yuruhiya/programming/library/Utility/Scanner.cpp"
#include <iostream>
#line 6 "/home/yuruhiya/programming/library/Utility/Scanner.cpp"
#include <tuple>
#include <type_traits>
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#define fwrite_unlocked fwrite
#define fflush_unlocked fflush
#endif
class Scanner {
    static int gc() {
        return getchar_unlocked();
    }
    static char next_char() {
        char c;
        scan(c);
        return c;
    }
    template <class T> static void scan(T& v) {
        std::cin >> v;
    }
    static void scan(char& v) {
        while (std::isspace(v = gc()))
            ;
    }
    static void scan(bool& v) {
        v = next_char() != '0';
    }
    static void scan(std::vector<bool>::reference v) {
        bool b;
        scan(b);
        v = b;
    }
    static void scan(std::string& v) {
        v.clear();
        for (char c = next_char(); !std::isspace(c); c = gc()) v += c;
    }
    static void scan(int& v) {
        v = 0;
        bool neg = false;
        char c = next_char();
        if (c == '-') {
            neg = true;
            c = gc();
        }
        for (; std::isdigit(c); c = gc()) v = v * 10 + (c - '0');
        if (neg) v = -v;
    }
    static void scan(long long& v) {
        v = 0;
        bool neg = false;
        char c = next_char();
        if (c == '-') {
            neg = true;
            c = gc();
        }
        for (; std::isdigit(c); c = gc()) v = v * 10 + (c - '0');
        if (neg) v = -v;
    }
    static void scan(double& v) {
        v = 0;
        double dp = 1;
        bool neg = false, after_dp = false;
        char c = next_char();
        if (c == '-') {
            neg = true;
            c = gc();
        }
        for (; std::isdigit(c) || c == '.'; c = gc()) {
            if (c == '.') {
                after_dp = true;
            } else if (after_dp) {
                v += (c - '0') * (dp *= 0.1);
            } else {
                v = v * 10 + (c - '0');
            }
        }
        if (neg) v = -v;
    }
    static void scan(long double& v) {
        v = 0;
        long double dp = 1;
        bool neg = false, after_dp = false;
        char c = next_char();
        if (c == '-') {
            neg = true;
            c = gc();
        }
        for (; std::isdigit(c) || c == '.'; c = gc()) {
            if (c == '.') {
                after_dp = true;
            } else if (after_dp) {
                v += (c - '0') * (dp *= 0.1);
            } else {
                v = v * 10 + (c - '0');
            }
        }
        if (neg) v = -v;
    }
    template <class T, class U> static void scan(std::pair<T, U>& v) {
        scan(v.first);
        scan(v.second);
    }
    template <class T, std::enable_if_t<!std::is_same_v<bool, T>, std::nullptr_t> = nullptr>
    static void scan(std::vector<T>& v) {
        for (auto& e : v) scan(e);
    }
    template <class T, std::enable_if_t<std::is_same_v<bool, T>, std::nullptr_t> = nullptr>
    static void scan(std::vector<T>& v) {
        for (auto e : v) scan(e);
    }
    template <std::size_t N = 0, class T> static void scan_tuple_impl(T& v) {
        if constexpr (N < std::tuple_size_v<T>) {
            scan(std::get<N>(v));
            scan_tuple_impl<N + 1>(v);
        }
    }
    template <class... T> static void scan(std::tuple<T...>& v) {
        scan_tuple_impl(v);
    }
    struct Read2DVectorHelper {
        std::size_t h, w;
        Read2DVectorHelper(std::size_t _h, std::size_t _w) : h(_h), w(_w) {}
        template <class T> operator std::vector<std::vector<T>>() {
            std::vector vector(h, std::vector<T>(w));
            scan(vector);
            return vector;
        }
    };
    struct ReadVectorHelper {
        std::size_t n;
        ReadVectorHelper(std::size_t _n) : n(_n) {}
        template <class T> operator std::vector<T>() {
            std::vector<T> vector(n);
            scan(vector);
            return vector;
        }
        auto operator[](std::size_t m) {
            return Read2DVectorHelper(n, m);
        }
    };
public:
    template <class T> T read() const {
        T result;
        scan(result);
        return result;
    }
    template <class T> auto read(std::size_t n) const {
        std::vector<T> result(n);
        scan(result);
        return result;
    }
    template <class T> auto read(std::size_t h, std::size_t w) const {
        std::vector result(h, std::vector<T>(w));
        scan(result);
        return result;
    }
    std::string read_line() const {
        std::string v;
        for (char c = gc(); c != '\n' && c != '\0'; c = gc()) v += c;
        return v;
    }
    template <class T> operator T() const {
        return read<T>();
    }
    int operator--(int) const {
        return read<int>() - 1;
    }
    auto operator[](std::size_t n) const {
        return ReadVectorHelper(n);
    }
    auto operator[](const std::pair<std::size_t, std::size_t>& nm) const {
        return Read2DVectorHelper(nm.first, nm.second);
    }
    void operator()() const {}
    template <class H, class... T> void operator()(H&& h, T&&... t) const {
        scan(h);
        operator()(std::forward<T>(t)...);
    }
private:
    template <template <class...> class, class...> struct Column;
    template <template <class...> class V, class Head, class... Tail>
    struct Column<V, Head, Tail...> {
        template <class... Args> using vec = V<std::vector<Head>, Args...>;
        using type = typename Column<vec, Tail...>::type;
    };
    template <template <class...> class V> struct Column<V> { using type = V<>; };
    template <class... T> using column_t = typename Column<std::tuple, T...>::type;
    template <std::size_t N = 0, class T> void column_impl(T& t) const {
        if constexpr (N < std::tuple_size_v<T>) {
            auto& vec = std::get<N>(t);
            using V = typename std::remove_reference_t<decltype(vec)>::value_type;
            vec.push_back(read<V>());
            column_impl<N + 1>(t);
        }
    }
public:
    template <class... T> auto column(std::size_t h) const {
        column_t<T...> result;
        while (h--) column_impl(result);
        return result;
    }
} in;
#define inputs(T, ...) \
    T __VA_ARGS__;     \
    in(__VA_ARGS__)
#define ini(...) inputs(int, __VA_ARGS__)
#define inl(...) inputs(long long, __VA_ARGS__)
#define ins(...) inputs(std::string, __VA_ARGS__)
#line 5 "/home/yuruhiya/programming/library/Utility/Printer.cpp"
#include <array>
#line 7 "/home/yuruhiya/programming/library/Utility/Printer.cpp"
#include <string_view>
#include <optional>
#include <charconv>
#include <cstring>
#include <cassert>
class Printer {
public:
    struct BoolString {
        std::string_view t, f;
        BoolString(std::string_view _t, std::string_view _f) : t(_t), f(_f) {}
    };
    struct Separator {
        std::string_view div, sep, last;
        Separator(std::string_view _div, std::string_view _sep, std::string_view _last)
            : div(_div), sep(_sep), last(_last) {}
    };
    inline static const BoolString Yes{"Yes", "No"}, yes{"yes", "no"}, YES{"YES", "NO"},
        Int{"1", "0"}, Possible{"Possible", "Impossible"};
    inline static const Separator space{" ", " ", "\n"}, no_space{"", "", "\n"},
        endl{"\n", "\n", "\n"}, comma{",", ",", "\n"}, no_endl{" ", " ", ""},
        sep_endl{" ", "\n", "\n"};
    BoolString bool_str{Yes};
    Separator separator{space};
    void print(int v) const {
        char buf[12]{};
        if (auto [ptr, e] = std::to_chars(std::begin(buf), std::end(buf), v);
            e == std::errc{}) {
            print(std::string_view(buf, ptr - buf));
        } else {
            assert(false);
        }
    }
    void print(long long v) const {
        char buf[21]{};
        if (auto [ptr, e] = std::to_chars(std::begin(buf), std::end(buf), v);
            e == std::errc{}) {
            print(std::string_view(buf, ptr - buf));
        } else {
            assert(false);
        }
    }
    void print(bool v) const {
        print(v ? bool_str.t : bool_str.f);
    }
    void print(std::vector<bool>::reference v) const {
        print(v ? bool_str.t : bool_str.f);
    }
    void print(char v) const {
        putchar_unlocked(v);
    }
    void print(std::string_view v) const {
        fwrite_unlocked(v.data(), sizeof(std::string_view::value_type), v.size(), stdout);
    }
    void print(double v) const {
        std::printf("%.20f", v);
    }
    void print(long double v) const {
        std::printf("%.20Lf", v);
    }
    template <class T> void print(const T& v) const {
        std::cout << v;
    }
    template <class T, class U> void print(const std::pair<T, U>& v) const {
        print(v.first);
        print(separator.div);
        print(v.second);
    }
    template <class T> void print(const std::optional<T>& v) const {
        print(*v);
    }
    template <class InputIterater>
    void print_range(const InputIterater& begin, const InputIterater& end) const {
        for (InputIterater i = begin; i != end; ++i) {
            if (i != begin) print(separator.sep);
            print(*i);
        }
    }
    template <class T> void print(const std::vector<T>& v) const {
        print_range(v.begin(), v.end());
    }
    template <class T, std::size_t N> void print(const std::array<T, N>& v) const {
        print_range(v.begin(), v.end());
    }
    template <class T> void print(const std::vector<std::vector<T>>& v) const {
        for (std::size_t i = 0; i < v.size(); ++i) {
            if (i) print(separator.last);
            print(v[i]);
        }
    }
    Printer() = default;
    Printer(const BoolString& _bool_str, const Separator& _separator)
        : bool_str(_bool_str), separator(_separator) {}
    Printer& operator()() {
        print(separator.last);
        return *this;
    }
    template <class Head> Printer& operator()(Head&& head) {
        print(head);
        print(separator.last);
        return *this;
    }
    template <class Head, class... Tail> Printer& operator()(Head&& head, Tail&&... tail) {
        print(head);
        print(separator.sep);
        return operator()(std::forward<Tail>(tail)...);
    }
    template <class... Args> Printer& flag(bool f, Args&&... args) {
        if (f) {
            return operator()(std::forward<Args>(args)...);
        } else {
            return *this;
        }
    }
    template <class InputIterator>
    Printer& range(const InputIterator& begin, const InputIterator& end) {
        print_range(begin, end);
        print(separator.last);
        return *this;
    }
    template <class Container> Printer& range(const Container& a) {
        range(a.begin(), a.end());
        return *this;
    }
    template <class... T> void exit(T&&... t) {
        operator()(std::forward<T>(t)...);
        std::exit(EXIT_SUCCESS);
    }
    Printer& flush() {
        fflush_unlocked(stdout);
        return *this;
    }
    Printer& set(const BoolString& _bool_str) {
        bool_str = _bool_str;
        return *this;
    }
    Printer& set(const Separator& _separator) {
        separator = _separator;
        return *this;
    }
    Printer& set(std::string_view t, std::string_view f) {
        bool_str = BoolString(t, f);
        return *this;
    }
} out;
#line 2 "/home/yuruhiya/programming/library/Utility/functions.cpp"
#include <algorithm>
#include <numeric>
#include <cmath>
#line 8 "/home/yuruhiya/programming/library/Utility/functions.cpp"
template <class T = long long> constexpr T TEN(std::size_t n) {
    T result = 1;
    for (std::size_t i = 0; i < n; ++i) result *= 10;
    return result;
}
template <
    class T, class U,
    std::enable_if_t<std::is_integral_v<T> && std::is_integral_v<U>, std::nullptr_t> = nullptr>
constexpr auto div_ceil(T n, U m) {
    return (n + m - 1) / m;
}
template <class T, class U> constexpr auto div_ceil2(T n, U m) {
    return div_ceil(n, m) * m;
}
template <class T> constexpr T triangle(T n) {
    return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1);
}
template <class T> constexpr T nC2(T n) {
    return (n & 1) ? (n - 1) / 2 * n : n / 2 * (n - 1);
}
template <class T, class U> constexpr auto middle(const T& l, const U& r) {
    return l + (r - l) / 2;
}
template <class T, class U, class V>
constexpr bool in_range(const T& v, const U& lower, const V& upper) {
    return lower <= v && v < upper;
}
template <class T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
constexpr bool is_square(T n) {
    T s = std::sqrt(n);
    return s * s == n || (s + 1) * (s + 1) == n;
}
template <class T = long long> constexpr T BIT(int b) {
    return T(1) << b;
}
template <class T> constexpr int BIT(T x, int i) {
    return (x & (T(1) << i)) ? 1 : 0;
}
template <class T> constexpr int Sgn(T x) {
    return (0 < x) - (0 > x);
}
template <class T> bool is_leap(T year) {
    return !(year % 4) && (year % 100 || !(year % 400));
}
template <class T, class U, std::enable_if_t<std::is_integral_v<U>, std::nullptr_t> = nullptr>
constexpr T Pow(T a, U n) {
    assert(n >= 0);
    T result = 1;
    while (n > 0) {
        if (n & 1) {
            result *= a;
            n--;
        } else {
            a *= a;
            n >>= 1;
        }
    }
    return result;
}
template <class T, class U, std::enable_if_t<std::is_integral_v<U>, std::nullptr_t> = nullptr>
constexpr T Powmod(T a, U n, T mod) {
    assert(n >= 0);
    if (a > mod) a %= mod;
    T result = 1;
    while (n > 0) {
        if (n & 1) {
            result = result * a % mod;
            n--;
        } else {
            a = a * a % mod;
            n >>= 1;
        }
    }
    return result;
}
template <class T> bool chmax(T& a, const T& b) {
    return a < b ? a = b, true : false;
}
template <class T> bool chmin(T& a, const T& b) {
    return a > b ? a = b, true : false;
}
template <class T> int sz(const T& v) {
    return v.size();
}
template <class T, class U> int lower_index(const T& a, const U& v) {
    return std::lower_bound(a.begin(), a.end(), v) - a.begin();
}
template <class T, class U> int upper_index(const T& a, const U& v) {
    return std::upper_bound(a.begin(), a.end(), v) - a.begin();
}
template <class T, class U = typename T::value_type> U Gcdv(const T& v) {
    return std::accumulate(std::next(v.begin()), v.end(), U(*v.begin()), std::gcd<U, U>);
}
template <class T, class U = typename T::value_type> U Lcmv(const T& v) {
    return std::accumulate(std::next(v.begin()), v.end(), U(*v.begin()), std::lcm<U, U>);
}
template <class T> T& Concat(T& v, const T& vec) {
    v.insert(v.end(), vec.begin(), vec.end());
    return v;
}
namespace internal {
    template <class T, std::size_t N>
    auto make_vector(std::vector<int>& sizes, const T& init) {
        if constexpr (N == 1) {
            return std::vector(sizes[0], init);
        } else {
            int size = sizes[N - 1];
            sizes.pop_back();
            return std::vector(size, make_vector<T, N - 1>(sizes, init));
        }
    }
}  // namespace internal
template <class T, std::size_t N>
auto make_vector(const int (&sizes)[N], const T& init = T()) {
    std::vector s(std::rbegin(sizes), std::rend(sizes));
    return internal::make_vector<T, N>(s, init);
}
namespace lambda {
    auto char_to_int = [](char c) {
        return c - '0';
    };
    auto lower_to_int = [](char c) {
        return c - 'a';
    };
    auto upper_to_int = [](char c) {
        return c - 'A';
    };
    auto int_to_char = [](int i) -> char {
        return '0' + i;
    };
    auto int_to_lower = [](int i) -> char {
        return 'a' + i;
    };
    auto int_to_upper = [](int i) -> char {
        return 'A' + i;
    };
    auto is_odd = [](auto n) {
        return n % 2 == 1;
    };
    auto is_even = [](auto n) {
        return n % 2 == 0;
    };
    auto is_positive = [](auto n) {
        return n > 0;
    };
    auto is_negative = [](auto n) {
        return n < 0;
    };
    auto increment = [](auto n) {
        return ++n;
    };
    auto decrement = [](auto n) {
        return --n;
    };
    auto self = [](const auto& n) {
        return n;
    };
    auto first = [](const auto& n) {
        return n.first;
    };
    auto second = [](const auto& n) {
        return n.second;
    };
    template <class T> auto cast() {
        return [](const auto& n) {
            return static_cast<T>(n);
        };
    };
    template <class T> auto equal_to(const T& x) {
        return [x](auto y) {
            return x == y;
        };
    }
    template <std::size_t I> auto get() {
        return [](const auto& n) {
            return std::get<I>(n);
        };
    }
    template <class F> auto cmp(F&& f) {
        return [f](const auto& a, const auto& b) {
            return f(a) < f(b);
        };
    }
}  // namespace lambda
#line 6 "/home/yuruhiya/programming/library/template_no_Ruby.cpp"
#if __has_include(<library/dump.hpp>)
#include <library/dump.hpp>
#define LOCAL
#else
#define dump(...) ((void)0)
#define dump2(...) ((void)0)
#endif
#line 2 "/home/yuruhiya/programming/library/Utility/oj_local.cpp"
template <class T> constexpr T oj_local(const T& oj, const T& local) {
#ifndef LOCAL
    return oj;
#else
    return local;
#endif
}
#line 14 "/home/yuruhiya/programming/library/template_no_Ruby.cpp"
#include <bits/stdc++.h>
#line 7 "/home/yuruhiya/programming/library/math/modint.cpp"
template <int MOD> struct modint {
    using value_type = long long;
private:
    value_type n;
public:
    constexpr static modint factorial(int n) {
        assert(n >= 0);
        modint result = 1;
        for (int i = 1; i <= n; ++i) {
            result *= i;
        }
        return result;
    }
    constexpr modint(const value_type x = 0) : n(x % MOD) {
        if (n < 0) n += MOD;
    }
    constexpr value_type value() const {
        return n;
    }
    constexpr int mod() const {
        return MOD;
    }
    constexpr modint operator+() const {
        return *this;
    }
    constexpr modint operator-() const {
        return n ? MOD - n : 0;
    }
    constexpr modint& operator++() {
        if (MOD <= ++n) n = 0;
        return *this;
    }
    constexpr modint& operator--() {
        if (n <= 0) n = MOD;
        n--;
        return *this;
    }
    constexpr modint operator++(int) {
        modint t = *this;
        ++*this;
        return t;
    }
    constexpr modint operator--(int) {
        modint t = *this;
        --*this;
        return t;
    }
    constexpr modint next() const {
        return ++modint(*this);
    }
    constexpr modint pred() const {
        return --modint(*this);
    }
    constexpr modint& operator+=(const modint& m) {
        n += m.n;
        if (n >= MOD) n -= MOD;
        return *this;
    }
    constexpr modint& operator-=(const modint& m) {
        n -= m.n;
        if (n < 0) n += MOD;
        return *this;
    }
    constexpr modint& operator*=(const modint& m) {
        n = n * m.n % MOD;
        return *this;
    }
    constexpr modint& operator/=(const modint& m) {
        value_type a = m.n, b = MOD, u = 1, v = 0;
        while (b) {
            value_type t = a / b;
            a -= t * b;
            std::swap(a, b);
            u -= t * v;
            std::swap(u, v);
        }
        n = n * u % MOD;
        if (n < 0) n += MOD;
        return *this;
    }
    constexpr bool operator==(const modint& m) const {
        return n == m.n;
    }
    constexpr bool operator!=(const modint& m) const {
        return n != m.n;
    }
    template <class M> constexpr modint pow(M m) const {
        if (0 <= m) {
            modint t = n, result = 1;
            while (m > 0) {
                if (m & 1) {
                    result *= t;
                    m--;
                } else {
                    t *= t;
                    m >>= 1;
                }
            }
            return result;
        } else {
            return (modint(1) / n).pow(-m);
        }
    }
    friend constexpr modint operator+(const modint& a, const modint& b) {
        return modint(a) += b;
    }
    friend constexpr modint operator-(const modint& a, const modint& b) {
        return modint(a) -= b;
    }
    friend constexpr modint operator*(const modint& a, const modint& b) {
        return modint(a) *= b;
    }
    friend constexpr modint operator/(const modint& a, const modint& b) {
        return modint(a) /= b;
    }
    friend std::ostream& operator<<(std::ostream& os, const modint<MOD>& m) {
        return os << m.value();
    }
    friend std::istream& operator>>(std::istream& is, modint<MOD>& m) {
        modint<MOD>::value_type x;
        is >> x;
        m = modint(x);
        return is;
    }
};
using mint = modint<get_MOD()>;
using VM = std::vector<mint>;
mint operator""_m(unsigned long long n) {
    return n;
}
#line 4 "/home/yuruhiya/programming/library/math/Combination.cpp"
template <int MOD, std::size_t N> class Combination {
    using value_type = modint<MOD>;
    std::array<value_type, N + 1> fac, finv, inv;
public:
    constexpr Combination() {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (std::size_t i = 2; i <= N; ++i) {
            fac[i] = fac[i - 1] * i;
            inv[i] = -inv[MOD % i] * (MOD / i);
            finv[i] = finv[i - 1] * inv[i];
        }
    }
    constexpr value_type P(int n, int r) const {
        return (n < r || n < 0 || r < 0) ? 0 : fac[n] * finv[n - r];
    }
    constexpr value_type C(int n, int r) const {
        return (n < r || n < 0 || r < 0) ? 0 : fac[n] * finv[r] * finv[n - r];
    }
    constexpr value_type H(int n, int r) const {
        return (n < 0 || r < 0) ? 0 : r == 0 ? 1 : C(n + r - 1, r);
    }
    constexpr value_type fact(int n) const {
        return fac[n];
    }
};
#line 4 "a.cpp"
using namespace std;
Combination<MOD, 2000009> C;
int main() {
    inl(n, m, d1, d2);
    ll d = d2 - d1;
    ll sum = m - d1 * (n - 1) - 1;
    mint ans = sum >= 0 ? C.C(sum + n, sum) : 0;
    FOR(x, 1, n) {
        ll sum2 = sum - (d + 1) * x;
        mint val = sum2 >= 0 ? C.C(n - 1, x) * C.C(sum2 + n, sum2) : 0;
        if (x % 2 == 1) {
            ans -= val;
        } else {
            ans += val;
        }
    }
    out(ans);
}
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