#define _CRT_SECURE_NO_WARNINGS #define _USE_MATH_DEFINES #define _SILENCE_CXX17_RESULT_OF_DEPRECATION_WARNING #include "bits/stdc++.h" #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 sz(x) ((int)(x).size()) #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 namespace std; using LL = long long; using ld = long double; using VB = vector; using VVB = vector; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using VS = vector; using VD = vector; using PII = pair; using VP = vector; using PLL = pair; using VPL = vector; templateusing Grid = vector>; templateusing PQ = priority_queue; templateusing PQS = priority_queue, greater>; constexpr int inf = (int)1e9; constexpr LL inf_ll = (LL)1e18, MOD = 1000000007; constexpr ld PI = M_PI, EPS = 1e-12; templateinline void Sort(T& a)noexcept { sort(all(a)); } templateinline void RSort(T& a)noexcept { sort(rall(a)); } templateinline void Reverse(T& a)noexcept { reverse(all(a)); } templateinline void Unique(T& a)noexcept { a.erase(unique(all(a)), a.end()); } templateinline T Sorted(T a)noexcept { Sort(a); return a; } templateinline T RSorted(T a)noexcept { RSort(a); return a; } templateinline T Reversed(T a)noexcept { Reverse(a); return a; } templateinline T Uniqued(T a)noexcept { Unique(a); return a; } templateinline auto Max(const T& a)noexcept { return *max_element(all(a)); } templateinline auto Min(const T& a)noexcept { return *min_element(all(a)); } templateinline int MaxPos(const T& a)noexcept { return max_element(all(a)) - a.begin(); } templateinline int MinPos(const T& a)noexcept { return min_element(all(a)) - a.begin(); } templateinline int Count(const T& a, const U& v)noexcept { return count(all(a), v); } templateinline int Find(const T& a, const U& v)noexcept { return find(all(a), v) - a.begin(); } templateinline U Sum(const T& a, const U& v)noexcept { return accumulate(all(a), v); } templateinline int Lower(const T& a, const U& v)noexcept { return lower_bound(all(a), v) - a.begin(); } templateinline int Upper(const T& a, const U& v)noexcept { return upper_bound(all(a), v) - a.begin(); } templateinline void RemoveIf(T& a, P f)noexcept { a.erase(remove_if(all(a), f), a.end()); } templateinline T Age(T n, T m)noexcept { return (n + m - 1) / m; } templateinline T Age2(T n, T m)noexcept { return Age(n, m) * m; } templateinline T Tri(T n)noexcept { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); } templateinline T BIT(int b)noexcept { return T{ 1 } << b; } templateinline T Gcd(T n, T m)noexcept { return m ? Gcd(m, n % m) : n; } templateinline T Lcm(T n, T m)noexcept { return n / Gcd(n, m) * m; } templateinline U Gcd2(const T& v)noexcept { return accumulate(next(v.begin()), v.end(), U(*v.begin()), Gcd); } templateinline U Lcm2(const T& v)noexcept { return accumulate(next(v.begin()), v.end(), U(*v.begin()), Lcm); } templateinline T Pow(T a, T n)noexcept { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; }return r; } templateinline T Powmod(T a, T n, T m = MOD)noexcept { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; } templateinline bool chmax(T& a, const T& b)noexcept { if (a < b) { a = b; return true; } return false; } templateinline bool chmin(T& a, const T& b)noexcept { if (a > b) { a = b; return true; } return false; } templateinline bool inRange(const T& v, const T& min, const T& max)noexcept { return min <= v && v <= max; } inline string operator*(string s, int n)noexcept { string ret; rep(i, n)ret += s; return ret; } // --- input --- // #if defined(_WIN32) || defined(ONLINE_JUDGE) #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #endif inline int gc()noexcept { return getchar_unlocked(); } templateinline void InputF(T& v)noexcept { cin >> v; } inline void InputF(char& v)noexcept { while (isspace(v = gc())); } inline void InputF(bool& v)noexcept { char c; InputF(c); v = c == '1'; } inline void InputF(string& v)noexcept { char c; for (InputF(c); !isspace(c); c = gc())v += c; } inline void InputF(int& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } inline void InputF(long long& v)noexcept { bool neg = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c); c = gc())v = v * 10 + (c - '0'); if (neg)v = -v; } inline void InputF(double& v)noexcept { double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c); if (c == '-') { neg = true; c = gc(); } for (; isdigit(c) || c == '.'; c = gc()) { if (c == '.')adp = true; else if (adp)v += (c - '0') * (dp *= 0.1); else v = v * 10 + (c - '0'); } if (neg)v = -v; } templateinline void InputF(pair& v)noexcept { InputF(v.first); InputF(v.second); } templateinline void InputF(vector& v)noexcept { for (auto& e : v)InputF(e); } templateinline T InputF() { T v; InputF(v); return v; } struct InputV { int n, m; InputV(int N) :n(N), m(0) {} InputV(pair N) :n(N.first), m(N.second) {} templateoperator vector()noexcept { vector v(n); InputF(v); return v; } templateoperator vector>()noexcept { vector> v(n, vector(m)); InputF(v); return v; } }; struct Input { templateoperator T()noexcept { return InputF(); } int operator--(int) { int v; InputF(v); v--; return v; } InputV operator[](int n)noexcept { return InputV(n); } InputV operator[](pair n)noexcept { return InputV(n); } void operator()() {} templatevoid operator()(H&& h, T&& ...t) { InputF(h); operator()(forward(t)...); } templatearray, W> get(int H) { array, W> ret; for (int i = 0; i < H; ++i)for (int j = 0; j < W; ++j)ret[j].push_back(InputF()); return ret; } }in; #define input(type) InputF() // --- output --- // struct BoolStr { const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {} }Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0"); struct DivStr { const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {} }spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", ""); class Output { BoolStr B{ Yes }; DivStr D{ spc }; bool isPrint = true; void p(double v) { printf("%.20f", v); } void p(long double v) { printf("%.20Lf", v); } void p(int v) { printf("%d", v); } void p(LL v) { printf("%lld", v); } void p(char v) { putchar(v); } void p(bool v) { printf("%s", v ? B.t : B.f); } templatevoid p(const T& v) { cout << v; } templatevoid p(const pair& v) { p(v.first); printf("%s", D.d); p(v.second); } templatevoid p(const vector& v) { rep(i, sz(v)) { if (i)printf("%s", D.d); p(v[i]); } } templatevoid p(const vector>& v) { rep(i, sz(v)) { if (i)printf("%s", D.l); p(v[i]); } } void p(const BoolStr& v) { B = v; isPrint = false; } void p(const DivStr& v) { D = v; isPrint = false; } public: Output& operator()() { printf("%s", D.l); return *this; } templateOutput& operator()(H&& h) { p(h); if (isPrint)printf("%s", D.l); isPrint = true; return *this; } templateOutput& operator()(H&& h, T&& ...t) { p(h); if (isPrint)printf("%s", D.d); isPrint = true; return operator()(forward(t)...); } templatevoid exit(T&& ...t) { operator()(forward(t)...); std::exit(EXIT_SUCCESS); } Output& flush() { cout.flush(); return *this; } Output& set_bs(const char* t, const char* f) { B = BoolStr(t, f); return *this; } }out; // --- dump --- // #if __has_include("dump.hpp") #include "dump.hpp" #else #define dump(...) (void(0)) #endif templatestruct Step { class It { T a, b, c; public: constexpr It() : a(T()), b(T()), c(T()) {} constexpr It(T _b, T _c, T _s) : a(_b), b(_c), c(_s) {} constexpr It& operator++() { --b; a += c; return *this; } constexpr It operator++(int) { It tmp = *this; --b; a += c; return tmp; } constexpr const T& operator*()const { return a; } constexpr const T* operator->()const { return &a; } constexpr bool operator==(const It& other)const { return b == other.b; } constexpr bool operator!=(const It& other)const { return !(b == other.b); } constexpr T start()const { return a; } constexpr T count()const { return b; } constexpr T step()const { return c; } }; constexpr Step(T b, T c, T s) : be(b, c, s) {} constexpr It begin()const { return be; } constexpr It end()const { return en; } constexpr T start()const { return be.start(); } constexpr T count()const { return be.count(); } constexpr T step()const { return be.step(); } operator vector()const { return as_vector(); } vector as_vector()const { vector res; res.reserve(count()); each([&](T i) {res.push_back(i); }); return res; } templatevoid each(F f)const { for (T i : *this)f(i); } templateauto map(F f)const { vector>> res; res.reserve(count()); each([&](T i) {res.push_back(f(i)); }); return res; } templateint count_if(F f)const { int res = 0; each([&](T i) {i += f(i); }); return res; } templatevector select(F f)const { vector res; each([&](T i) {if (f(i))res.push_back(i); }); return res; } templateauto sum(F f)const { decay_t> res = 0; each([&](T i) {res += f(i); }); return res; } using value_type = T; using iterator = It; private: It be, en; }; templateinline constexpr auto step(T a) { return Step(0, a, 1); } templateinline constexpr auto step(T a, T b) { return Step(a, b - a, 1); } templateinline constexpr auto step(T a, T b, T c) { return Step(a, (b - a - 1) / c + 1, c); } templateauto MakeVector(size_t size, F f) { vector>> res(size); for (size_t i = 0; i < size; ++i)res[i] = f(i); return res; } templateT Slice(const T& v, size_t i, size_t len) { return i < v.size() ? T(v.begin() + i, v.begin() + min(i + len, v.size())) : T(); } templatevoid Each(T& v, F f) { for (auto& e : v)f(e); } templateauto Map(const T& v, F f) { vector>> res(v.size()); size_t i = 0; for (const auto& e : v)res[i++] = f(e); return res; } templateauto MapIndex(const T& v, F f) { vector>> res(v.size()); size_t i = 0; for (auto it = v.begin(); it != v.end(); ++it, ++i)res[i] = f(i, *it); return res; } templateauto Select(const T& v, F f) { T res; for (const auto& e : v)if (f(e))res.push_back(e); return res; } templatevector TrueIndex(const T& v, F f) { vector res; size_t i = 0; for (const auto& e : v) { if (f(e))res.push_back(i); ++i; } return res; } // ---------------------------------------------------------------- // templatestruct modint { using T = long long; T n; constexpr modint(const T x = 0)noexcept :n(x% MOD) { if (n < 0)n += MOD; } constexpr int get_mod()const noexcept { return MOD; } constexpr modint operator+()const noexcept { return *this; } constexpr modint operator-()const noexcept { return n ? MOD - n : 0; } constexpr modint& operator++()noexcept { if (MOD <= ++n)n = 0; return *this; } constexpr modint& operator--()noexcept { if (n <= 0)n = MOD; n--; return *this; } constexpr modint& operator++(int)noexcept { modint t = *this; ++* this; return t; } constexpr modint& operator--(int)noexcept { modint t = *this; --* this; return t; } constexpr modint next()const noexcept { modint t = *this; ++t; return t; } constexpr modint pred()const noexcept { modint t = *this; --t; return t; } constexpr modint operator+(const modint& m)const noexcept { return modint(*this) += m; } constexpr modint operator-(const modint& m)const noexcept { return modint(*this) -= m; } constexpr modint operator*(const modint& m)const noexcept { return modint(*this) *= m; } constexpr modint operator/(const modint& m)const noexcept { return modint(*this) /= m; } constexpr modint& operator+=(const modint& m)noexcept { n += m.n; if (n >= MOD)n -= MOD; return *this; } constexpr modint& operator-=(const modint& m)noexcept { n -= m.n; if (n < 0)n += MOD; return *this; } constexpr modint& operator*=(const modint& m)noexcept { n = n * m.n % MOD; return *this; } constexpr modint& operator/=(const modint& m)noexcept { assert(m.n); T a = m.n, b = MOD, u = 1, v = 0; while (b) { T t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } n = n * u % MOD; if (n < 0)n += MOD; return *this; } constexpr bool operator==(const modint& m)const noexcept { return n == m.n; } constexpr bool operator!=(const modint& m)const noexcept { return n != m.n; } constexpr modint pow(modint m)const noexcept { modint t = n, res = 1; while (m.n > 0) { if (m.n & 1)res *= t; t *= t; m.n >>= 1; } return res; } constexpr modint operator^(modint m)const noexcept { return pow(m); } }; using mint = modint<1000000007>; using VM = vector; templateostream& operator<<(ostream& os, const modint& m)noexcept { return os << m.n; } templateistream& operator>>(istream& is, modint& m)noexcept { return is >> m.n; } mint operator""_m(unsigned long long n) { return n; } templateclass Imos { const int n; vector a; public: Imos(int _n) :n(_n), a(_n + 1) {} // [l, r) void add(int l, int r, T v = 1) { assert(0 <= l && l < r && r <= n); a[l] += v; a[r] -= v; } void build() { for (int i = 1; i < n; ++i) { a[i] += a[i - 1]; } } T operator[](int i)const { return a[i]; } const vector& get_a()const { return a; } }; int main() { int n, d, k; in(n, d, k); VM dp(k + 1); dp[0] = 1; rep(_, n) { Imos a(k + 1); rep(i, k) { a.add(i + 1, min(i + 1 + d, k + 1), dp[i]); } a.build(); dp = a.get_a(); } out(dp[k]); }