#line 1 "Library/src/debug.hpp" #ifdef ONLINE_JUDGE #define debug(x) void(0) #else #define _GLIBCXX_DEBUG #define debug(x) std::cerr << __LINE__ << " : " << #x << " = " << (x) << std::endl #endif #line 2 "Library/src/math/static_modint.hpp" #include #include #include #line 3 "Library/src/internal/type_traits.hpp" #include #include #include #line 7 "Library/src/internal/type_traits.hpp" namespace kyopro { namespace internal { template struct first_enabled {}; template struct first_enabled, Args...> { using type = T; }; template struct first_enabled, Args...> : first_enabled {}; template struct first_enabled { using type = T; }; template using first_enabled_t = typename first_enabled::type; template * = nullptr> struct int_least { using type = first_enabled_t, std::enable_if, std::enable_if, std::enable_if, std::enable_if>; }; template * = nullptr> struct uint_least { using type = first_enabled_t, std::enable_if, std::enable_if, std::enable_if, std::enable_if>; }; template using int_least_t = typename int_least::type; template using uint_least_t = typename uint_least::type; template using double_size_uint_t = uint_least_t<2 * std::numeric_limits::digits>; template using double_size_int_t = int_least_t<2 * std::numeric_limits::digits>; struct modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; // is_integral template using is_integral_t = std::enable_if_t || std::is_same_v || std::is_same_v>; }; // namespace internal }; // namespace kyopro /* * @ref https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8 */ #line 3 "Library/src/math/gcd.hpp" #include namespace kyopro { template constexpr inline T _gcd(T a, T b) noexcept { assert(a >= 0 && b >= 0); if (a == 0 || b == 0) return a + b; int d = std::min(__builtin_ctzll(a), __builtin_ctzll(b)); a >>= __builtin_ctzll(a), b >>= __builtin_ctzll(b); while (a != b) { if (!a || !b) { return a + b; } if (a >= b) { a -= b; a >>= __builtin_ctzll(a); } else { b -= a; b >>= __builtin_ctzll(b); } } return a << d; } template constexpr inline T ext_gcd(T a, T b, T& x, T& y) noexcept { x = 1, y = 0; T nx = 0, ny = 1; while (b) { T q = a / b; std::tie(a, b) = std::pair{b, a % b}; std::tie(x, nx) = std::pair{nx, x - nx * q}; std::tie(y, ny) = std::pair{ny, y - ny * q}; } return a; } }; // namespace kyopro #line 8 "Library/src/math/static_modint.hpp" namespace kyopro { template = 0>* = nullptr> class modint : internal::modint_base { using mint = modint<_mod>; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; u32 v; constexpr u32 normalize(i64 v_) const noexcept { v_ %= _mod; if (v_ < 0) { v_ += _mod; } return v_; } public: static constexpr u32 mod() noexcept { return _mod; } constexpr modint() noexcept : v(0) {} constexpr modint(i64 v_) noexcept : v(normalize(v_)) {} static mint raw(u32 a) { mint m; m.v = a; return m; } constexpr u32 val() const noexcept { return v; } constexpr mint& operator+=(const mint& rhs) noexcept { v += rhs.val(); if (v >= _mod) { v -= _mod; } return (*this); } constexpr mint& operator-=(const mint& rhs) noexcept { v += _mod - rhs.val(); if (v >= _mod) { v -= _mod; } return (*this); } constexpr mint& operator*=(const mint& rhs) noexcept { v = (u64)v * rhs.val() % _mod; return (*this); } constexpr mint operator+(const mint& r) const noexcept { return mint(*this) += r; } constexpr mint operator-(const mint& r) const noexcept { return mint(*this) -= r; } constexpr mint operator*(const mint& r) const noexcept { return mint(*this) *= r; } constexpr mint& operator+=(i64 rhs) noexcept { (*this) += mint(rhs); return (*this); } constexpr mint& operator-=(i64 rhs) noexcept { (*this) -= mint(rhs); return (*this); } constexpr mint& operator*=(i64 rhs) noexcept { (*this) *= mint(rhs); return (*this); } constexpr friend mint operator+(i64 l, const mint& r) noexcept { return mint(l) += r; } constexpr friend mint operator-(i64 l, const mint& r) noexcept { return mint(l) -= r; } constexpr friend mint operator*(i64 l, const mint& r) noexcept { return mint(l) *= r; } constexpr mint operator+(i64 r) const noexcept { return mint(*this) += r; } constexpr mint operator-(i64 r) const noexcept { return mint(*this) -= r; } constexpr mint operator*(i64 r) const noexcept { return mint(*this) *= r; } constexpr mint& operator=(i64 r) noexcept { return (*this) = mint(r); } constexpr bool operator==(const mint& r) const noexcept { return (*this).val() == r.val(); } template * = nullptr> constexpr mint pow(T e) const noexcept { mint ans(1), base(*this); while (e) { if (e & 1) { ans *= base; } base *= base; e >>= 1; } return ans; } constexpr mint inv() const noexcept { long long x, y; auto d = ext_gcd((long long)_mod, (long long)v, x, y); assert(d == 1); return mint(y); } constexpr mint& operator/=(const mint& r) noexcept { return (*this) *= r.inv(); } constexpr mint operator/(const mint& r) const noexcept { return mint(*this) *= r.inv(); } constexpr friend mint operator/(const mint& l, i64 r) noexcept { return mint(l) /= mint(r); } constexpr friend mint operator/(i64 l, const mint& r) noexcept { return mint(l) /= mint(r); } }; }; // namespace kyopro /** * @brief static modint */ #line 2 "Library/src/stream.hpp" #include #include #include #line 6 "Library/src/stream.hpp" namespace kyopro { inline void single_read(char& c) { c = getchar_unlocked(); while (isspace(c)) c = getchar_unlocked(); } template * = nullptr> inline void single_read(T& a) { a = 0; bool is_negative = false; char c = getchar_unlocked(); while (isspace(c)) { c = getchar_unlocked(); } if (c == '-') is_negative = true, c = getchar_unlocked(); while (isdigit(c)) { a = 10 * a + (c - '0'); c = getchar_unlocked(); } if (is_negative) a *= -1; } template * = nullptr> inline void single_read(T& a) { long long x; single_read(x); a = T(x); } inline void single_read(std::string& str) noexcept { char c = getchar_unlocked(); while (isspace(c)) c = getchar_unlocked(); while (!isspace(c)) { str += c; c = getchar_unlocked(); } } template inline void read(T& x) noexcept {single_read(x);} template inline void read(Head& head, Tail&... tail) noexcept { single_read(head), read(tail...); } inline void single_write(char c) noexcept { putchar_unlocked(c); } template * = nullptr> inline void single_write(T a) noexcept { if (!a) { putchar_unlocked('0'); return; } if constexpr (std::is_signed_v) { if (a < 0) putchar_unlocked('-'), a *= -1; } constexpr int d = std::numeric_limits::digits10; char s[d + 1]; int now = d + 1; while (a) { s[--now] = (char)'0' + a % 10; a /= 10; } while (now <= d) putchar_unlocked(s[now++]); } template * = nullptr> inline void single_write(T a) noexcept { single_write(a.val()); } inline void single_write(const std::string& str) noexcept { for (auto c : str) { putchar_unlocked(c); } } template inline void write(T x) noexcept { single_write(x); } template inline void write(Head head, Tail... tail) noexcept { single_write(head); putchar_unlocked(' '); write(tail...); } template inline void put(Args... x) noexcept { write(x...); putchar_unlocked('\n'); } }; // namespace kyopro /** * @brief 高速入出力 */ #line 2 "Library/src/template.hpp" #include #define rep(i, n) for (int i = 0; i < (n); i++) #define all(x) std::begin(x), std::end(x) #define popcount(x) __builtin_popcountll(x) using i128 = __int128_t; using ll = long long; using ld = long double; using graph = std::vector>; using P = std::pair; constexpr int inf = std::numeric_limits::max() / 2; constexpr ll infl = std::numeric_limits::max() / 2; const long double pi = acosl(-1); constexpr uint64_t MOD = 1e9 + 7; constexpr uint64_t MOD2 = 998244353; constexpr int dx[] = {1, 0, -1, 0, 1, -1, -1, 1, 0}; constexpr int dy[] = {0, 1, 0, -1, 1, 1, -1, -1, 0}; template constexpr inline bool chmax(T1& a, T2 b) { return a < b && (a = b, true); } template constexpr inline bool chmin(T1& a, T2 b) { return a > b && (a = b, true); } #line 5 "a.cpp" using namespace std; using namespace kyopro; using mint = modint<(int)1e9 + 7>; int main() { int n, s, k; read(n, s, k); vector dp(s + 1, mint()); rep(i, n) dp[n * i] = mint::raw(1); for (int i = 1; i < n; ++i) { vector ndp(s + 1, mint()); rep(t, s + 1) { for (int x = k; t + (n - i) * x <= s; ++x) { ndp[t + (n - i) * x] += dp[t]; } } swap(dp, ndp); } put(dp[s]); }