#line 2 "/Users/korogi/Desktop/cp-cpp/template.hpp" #include using namespace std; using i32 = int; using i64 = long long; using i128 = __int128; using u32 = unsigned int; using u64 = unsigned long long; using u128 = unsigned __int128; using f32 = double; using f64 = long double; #define DMP(x) cout << "[" << __LINE__ << "]" << " " << #x << ":" << " " << x << endl; #define FOR1(n) for(int _ = 0 , n_ = (n); _ < n_; _++) #define FOR2(i, n) for(int i = 0 , n_ = (n); i < n_; i++) #define FOR3(i, s, t) for(int i = (s), t_ = (t); i < t_; i++) #define FOR4(i, s, t, d) for(int i = (s), t_ = (t), d_ = (d); i < t_; i += d_) #define OVERLOAD4(a, b, c, d, e, ...) e #define FOR(...) OVERLOAD4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define REV1(n) for(int _ = (n) - 1; _ >= 0 ; _--) #define REV2(i, n) for(int i = (n) - 1; i >= 0 ; i--) #define REV3(i, s, t) for(int i = (t) - 1, s_ = (s); i >= s_; i--) #define REV4(i, s, t, d) for(int i = (t) - 1, s_ = (s), d_ = (d); i >= s_; i -= d_) #define OVERLOAD3(a, b, c, d, ...) d #define REV(...) OVERLOAD4(__VA_ARGS__, REV4, REV3, REV2, REV1)(__VA_ARGS__) #define FOR_SUBSET(T, S) for(int S_ = (S), T = S_; T >= 0; T = (T == 0 ? -1 : (T - 1) & S_)) #define MULTI for(int testcase_ = in(), testcase = 0; testcase < testcase_; testcase++) [&] template < class T > using heap_max = priority_queue< T, vector< T >, less< T > >; template < class T > using heap_min = priority_queue< T, vector< T >, greater< T >>; template < class T, class U > bool chmin(T& a, const U& b) { return a > b ? a = b, 1 : 0; } template < class T, class U > bool chmax(T& a, const U& b) { return a < b ? a = b, 1 : 0; } i64 floor_div(const i64 n, const i64 d) { assert(d != 0); return n / d - ((n ^ d) < 0 && n % d != 0); } i64 ceil_div(const i64 n, const i64 d) { assert(d != 0); return n / d + ((n ^ d) >= 0 && n % d != 0); } template < class T, class F > T bin_search(T ok, T ng, const F& check) { while((ok > ng ? ok - ng : ng - ok) > 1) { T mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; } template < class T, class F > T bin_search_real(T ok, T ng, const F& check, int step = 100) { FOR(step) { T mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; } template < class T, class U > T accum(const vector< U >& a) { return accumulate(a.begin(), a.end(), T(0)); } template < class T > void sort(vector< T >& a) { sort(a.begin(), a.end()); } template < class T > void rsort(vector< T >& a) { sort(a.rbegin(), a.rend()); } template < class T > void reverse(vector< T >& a) { reverse(a.begin(), a.end()); } void sort(string& s) { sort(s.begin(), s.end()); } void rsort(string& s) { sort(s.rbegin(), s.rend()); } void reverse(string& s) { reverse(s.begin(), s.end()); } template < class T, class Cmp > void sort(vector< T >& a, Cmp cmp) { sort(a.begin(), a.end(), cmp); } template < class T > int LB(const vector< T >& a, T x) { return distance(a.begin(), lower_bound(a.begin(), a.end(), x)); } template < class T > int UB(const vector< T >& a, T x) { return distance(a.begin(), upper_bound(a.begin(), a.end(), x)); } template < class T > void unique(vector< T >& a) { sort(a.begin(), a.end()); a.erase(unique(a.begin(), a.end()), a.end()); } vector iota(int n) { vector a(n); iota(a.begin(), a.end(), 0); return a; } istream& operator >> (istream& is, i128& x) { string s; is >> s; int m = (s[0] == '-'); x = 0; FOR(i, m, ssize(s)) x = x * 10 + (s[i] - '0'); if(m) x *= -1; return is; } ostream& operator << (ostream& os, const i128& x) { if(x == 0) return os << '0'; i128 y = x; if(y < 0) { os << '-'; y *= -1; } vector ny; while(y) ny.push_back(y % 10), y /= 10; REV(i, ssize(ny)) os << ny[i]; return os; } namespace scan { struct x0 { template < class T > operator T() { T x; cin >> x; return x; } }; struct x1 { int n; x1(int n) : n(n) {} template < class T > operator vector< T >() { vector< T > a(n); for(T& x : a) cin >> x; return a; } }; struct x2 { int h, w; x2(int h, int w) : h(h), w(w) {} template < class T > operator vector< vector< T > >() { vector m(h, vector< T >(w)); for(vector< T >& a : m) for(T& x : a) cin >> x; return m; } }; struct cppio { cppio() { cin.tie(0); ios::sync_with_stdio(0); } } cppio_instance; } scan::x0 in() { return scan::x0(); } scan::x1 in(int n) { return scan::x1(n); } scan::x2 in(int h, int w) { return scan::x2(h, w); } template < class T > ostream& operator << (ostream& os, const vector< T >& a) { const int n = a.size(); FOR(i, n) { os << a[i]; if(i + 1 != n) os << ' '; } return os; } template < class T > int print_n(const vector< T >& a) { for(const T& x : a) cout << x << '\n'; return 0; } int print() { cout << '\n'; return 0; } template < class Head, class... Tail > int print(Head&& h, Tail&&... t) { cout << h; if(sizeof...(Tail)) cout << ' '; return print(forward(t)...); } namespace printer { void prec(int n) { cout << fixed << setprecision(n); } void flush() { cout.flush(); } } vector& operator ++ (vector& a) { for(auto& e : a) e++; return a; } vector& operator -- (vector& a) { for(auto& e : a) e--; return a; } vector operator ++ (vector& a, int) { vector b = a; ++a; return b; } vector operator -- (vector& a, int) { vector b = a; --a; return b; } template < class T > vector> RLE(const vector< T >& a) { vector> v; for(const T& x : a) { if(not v.empty() and v.back().first == x) v.back().second++; else v.emplace_back(x, 1); } return v; } vector> RLE(const string& s) { vector> v; for(const char& c : s) { if(not v.empty() and v.back().first == c) v.back().second++; else v.emplace_back(c, 1); } return v; } template < class String, class Same > vector RLE(const String& a, const Same same) { vector v; for(const auto& x : a) { if(not v.empty() and same(v.back().back(), x)) v.back().push_back(x); else v.push_back({x}); } return v; } int YESNO(bool yes) { return print(yes ? "YES" : "NO"); } int YesNo(bool yes) { return print(yes ? "Yes" : "No"); } int Yes() { return print("Yes"); } int No() { return print("No"); } constexpr i32 INF32 = 1e9; constexpr i64 INF64 = 1e18; template < class T > constexpr T infty = 0; template <> constexpr int infty = 1e9; template <> constexpr int infty = 1e9; template <> constexpr i64 infty = 1e18; template <> constexpr u64 infty = 1e18; namespace bit { int pop(int x) { return popcount(x); } int pop(u32 x) { return popcount(x); } int pop(i64 x) { return popcount(x); } int pop(u64 x) { return popcount(x); } int parity(int x) { return __builtin_parity(x); } int parity(u32 x) { return __builtin_parity(x); } int parity(i64 x) { return __builtin_parityll(x); } int parity(u64 x) { return __builtin_parityll(x); } int sgn(int x) { return parity(x) ? -1 : +1; } int sgn(u32 x) { return parity(x) ? -1 : +1; } int sgn(i64 x) { return parity(x) ? -1 : +1; } int sgn(u64 x) { return parity(x) ? -1 : +1; } int top(int x) { return x == 0 ? -1 : 31 - __builtin_clz(x); } int top(u32 x) { return x == 0 ? -1 : 31 - __builtin_clz(x); } int top(i64 x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } int top(u64 x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } int low(int x) { return x == 0 ? -1 : __builtin_ctz(x); } int low(u32 x) { return x == 0 ? -1 : __builtin_ctz(x); } int low(i64 x) { return x == 0 ? -1 : __builtin_ctzll(x); } int low(u64 x) { return x == 0 ? -1 : __builtin_ctzll(x); } int ceil(int x) { return bit_ceil(x); } i64 ceil(i64 x) { return bit_ceil(x); } int floor(int x) { return bit_floor(x); } i64 floor(i64 x) { return bit_floor(x); } } // (-1)^n int parity_sign(int n) { return n % 2 == 0 ? +1 : -1; } // template < class T > pair< T, int > min(const vector< T >& a) { auto itr = min_element(a.begin(), a.end()); return {*itr, itr - a.begin()}; } // template < class T > pair< T, int > max(const vector< T >& a) { auto itr = max_element(a.begin(), a.end()); return {*itr, itr - a.begin()}; } template < class Key, class Value > struct key_value { Key key; Value value; }; template < class Value > key_value min(const vector& a) { assert(1 <= ssize(a)); auto itr = min_element(a.begin(), a.end()); return {static_cast(distance(a.begin(), itr)), *itr}; } template < class Value > key_value max(const vector& a) { assert(1 <= ssize(a)); auto itr = max_element(a.begin(), a.end()); return {static_cast(distance(a.begin(), itr)), *itr}; } struct grid { int H, W; grid(int H, int W) : H(H), W(W) {} static constexpr pair dir4[] = { {-1, 0}, { 0, -1}, { 0, +1}, {+1, 0} }; static constexpr pair dir8[] = { {-1, -1}, {-1, 0}, {-1, +1}, { 0, -1}, { 0, +1}, {+1, -1}, {+1, 0}, {+1, +1} }; bool contains(int i, int j) const { return 0 <= i and i < H and 0 <= j and j < W; } template < class F > void for_each_dir4(int i, int j, const F& f) const { for(const auto [di, dj] : dir4) { const int ni = i + di, nj = j + dj; if(contains(ni, nj)) f(ni, nj); } } template < class F > void for_each_dir8(int i, int j, const F& f) const { for(const auto [di, dj] : dir8) { const int ni = i + di, nj = j + dj; if(contains(ni, nj)) f(ni, nj); } } }; template < class Sum > struct psum1D { int n; vector s; psum1D() : n(0), s(1, Sum()) {} template < class Value > psum1D(const vector& a) : n(ssize(a)), s(n + 1, Sum()) { FOR(i, n) s[i + 1] = s[i] + static_cast(a[i]); } // [l, r) Sum v(int l, int r) const { assert(0 <= l and l <= r and r <= n); return s[r] - s[l]; } void push_back(const Sum& x) { s.push_back(s.back() + x); n += 1; } }; template < class Value > struct psum2D { int H, W; vector> A; bool built; psum2D(int H, int W) : H(H), W(W), A(H + 1, vector(W + 1, Value(0))), built(false) {} // A[x][y] += v void add(int x, int y, Value v) { assert(not built); assert(0 <= x and x < H); assert(0 <= y and y < W); A[x + 1][y + 1] += v; } void build() { FOR(x, H) FOR(y, W + 1) A[x + 1][y] += A[x][y]; FOR(x, H + 1) FOR(y, W) A[x][y + 1] += A[x][y]; built = true; } // [xL, xR) * [yL, yR) Value sum(int xL, int xR, int yL, int yR) { assert(built); assert(0 <= xL and xL <= xR and xR <= H); assert(0 <= yL and yL <= yR and yR <= W); return A[xR][yR] - A[xR][yL] - A[xL][yR] + A[xL][yL]; } Value get(int x, int y) { assert(built); assert(0 <= x and x < H); assert(0 <= y and y < W); return sum(x, x + 1, y, y + 1); } }; template < class Value > struct imos2D { int H, W; vector> A; bool built; imos2D(int H, int W) : H(H), W(W), A(H + 1, vector(W + 1, Value(0))), built(false) {} void add(int xL, int xR, int yL, int yR, Value v) { assert(not built); assert(0 <= xL and xL <= xR and xR <= H); assert(0 <= yL and yL <= yR and yR <= W); A[xL][yL] += v; A[xR][yL] -= v; A[xL][yR] -= v; A[xR][yR] += v; } void build() { assert(not built); FOR(i, H + 1) FOR(j, W) A[i][j + 1] += A[i][j]; FOR(i, H) FOR(j, W + 1) A[i + 1][j] += A[i][j]; built = true; } Value get(int x, int y) { assert(built); assert(0 <= x and x < H); assert(0 <= y and y < W); return A[x][y]; } }; #line 3 "/Users/korogi/Desktop/cp-cpp/rnd.hpp" namespace rnd { u32 seed; mt19937 mt; struct gen_seed { gen_seed() { seed = random_device()(); mt = mt19937(seed); } } gen_seed_instance; // [L, R) template < class Int > Int i(Int L, Int R) { assert(L < R); return uniform_int_distribution(L, R - 1)(mt); } template < class Real > Real r(Real L, Real R) { assert(L <= R); return uniform_real_distribution(L, R)(mt); } } template < int n, array mod > struct hash_vector { array a; using hvec = hash_vector; hvec& s(array a) { FOR(i, n) this->a[i] = a[i] < mod[i] ? a[i] : a[i] - mod[i]; return *this; } hash_vector(u32 v = 0) { FOR(i, n) a[i] = v % mod[i] + mod[i]; s(a); } hvec operator - () const { return hvec() - *this; } hvec& operator += (const hvec& r) { FOR(i, n) a[i] += r.a[i]; return s(a); } hvec& operator -= (const hvec& r) { FOR(i, n) a[i] += mod[i] - r.a[i]; return s(a); } hvec& operator *= (const hvec& r) { FOR(i, n) a[i] = u64(a[i]) * r.a[i] % mod[i]; return *this; } hvec& operator /= (const hvec& r) { return *this *= inv(r); } hvec operator + (const hvec& r) const { return hvec(*this) += r; } hvec operator - (const hvec& r) const { return hvec(*this) -= r; } hvec operator * (const hvec& r) const { return hvec(*this) *= r; } hvec operator / (const hvec& r) const { return hvec(*this) /= r; } bool operator == (const hvec& r) const { return a == r.a; } bool operator != (const hvec& r) const { return a != r.a; } bool operator < (const hvec& r) const { return a < r.a; } }; template < int n, array mod > hash_vector pow(hash_vector x, u64 m) { hash_vector p(1); for(; m; m >>= 1) { if(m & 1) p *= x; x *= x; } return p; } template < int n, array mod > hash_vector inv(hash_vector x) { hash_vector res; FOR(i, n) { u32 a = x.a[i], b = mod[i], u = 1, v = 0; while(b) { u32 t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } res[i] = u; } return res; } template < int n, array mod > ostream& operator << (ostream& os, const hash_vector< n, mod >& x) { FOR(i, n) { if(i) os << ' '; os << x.a[i]; } return os; } using hvec1 = hash_vector< 1, array{999999937} >; using hvec2 = hash_vector< 2, array{999999937, 1000000007} >; using hvec3 = hash_vector< 3, array{999999937, 1000000007, 1000000009} >; using hvec4 = hash_vector< 4, array{999999937, 1000000007, 1000000009, 1000000021} >; #line 280 "/Users/korogi/Desktop/cp-cpp/template.hpp" namespace r52 { int abs(int x) { return x >= 0 ? x : -x; } i64 abs(i64 x) { return x >= 0 ? x : -x; } i128 abs(i128 x) { return x >= 0 ? x : -x; } } #line 2 "/Users/korogi/Desktop/cp-cpp/mod/dynamic_modint.hpp" template < int ID > struct dynamic_modint { inline static u32 mod = 998244353; using mint = dynamic_modint; u32 v; static void set_mod(u32 m) { assert(1 <= m); mod = m; } constexpr mint& s(u32 v) { this->v = v < mod ? v : v - mod; return *this; } dynamic_modint(i64 v = 0) { i64 x = v % mod; if(x < 0) x += mod; this->v = static_cast(x); } mint operator - () const { return mint() - *this; } mint operator + () const { return *this; } mint& operator += (const mint& r) { return s(v + r.v); } mint& operator -= (const mint& r) { return s(v + mod - r.v); } mint& operator *= (const mint& r) { v = u64(v) * r.v % mod; return *this; } mint& operator /= (const mint& r) { return *this *= inv(r); } mint operator + (const mint& r) const { return mint(*this) += r; } mint operator - (const mint& r) const { return mint(*this) -= r; } mint operator * (const mint& r) const { return mint(*this) *= r; } mint operator / (const mint& r) const { return mint(*this) /= r; } bool operator == (const mint& r) const { return v == r.v; } bool operator != (const mint& r) const { return v != r.v; } }; template < int ID > dynamic_modint pow(dynamic_modint x, u64 n) { dynamic_modint p(1); for(; n; n >>= 1) { if(n & 1) p *= x; x *= x; } return p; } template < int ID > dynamic_modint inv(dynamic_modint x) { int a = x.v, b = dynamic_modint::mod, u = 1, v = 0; while(b) { int t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return dynamic_modint(u); } template < int ID > istream& operator >> (istream& is, dynamic_modint& x) { i64 v; is >> v; x = dynamic_modint(v); return is; } template < int ID > ostream& operator << (ostream& os, const dynamic_modint& x) { return os << x.v; } using modint = dynamic_modint<-1>; #line 3 "a.cpp" int main() { int K = in(), S = in(), N = in(); using mint = dynamic_modint<-1>; mint::set_mod(10007); vector F(K + 1); F[0] = 1; F[1] = 1; for(int i = 2; i <= K; i++) F[i] = F[i - 1] + F[i - 2]; FOR(i, K + 1) F[i] = inv(F[i]); vector ans(N + 1); ans[0] = 0; ans[1] = S; for(int i = 2; i <= N; i++) { for(int j = 0; j <= K; j++) { if(0 <= i - j - 1) ans[i] += F[j] * ans[i - j - 1]; } } print(ans[N]); }