//#include //using namespace std; //using ll=long long; //const ll ILL=2167167167167167167; //const int INF=2100000000; //#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++) //#define all(p) p.begin(),p.end() //template using _pq = priority_queue, greater>; //template int LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} //template int UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} //template bool chmin(T &a,T b){if(b bool chmax(T &a,T b){if(a void So(vector &v) {sort(v.begin(),v.end());} //template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} //bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;} //template void vec_out(vector &p,int ty=0){ // if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'< T vec_min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} //template T vec_max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} //template T vec_sum(vector &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;} //int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;} //template T square(T a){return a * a;} // //#include "po167_library/fps/Multipoint_Evaluation.hpp" //#include "po167_library/math/Binomial.hpp" //using mint = atcoder::modint998244353; // // //void solve(); //// POP'N ROLL MUSIC / TOMOO //int main() { // ios::sync_with_stdio(false); // cin.tie(nullptr); // // int t = 1; // // cin >> t; // rep(i, 0, t) solve(); //} // //void solve(){ // int N, S, M; // cin >> N >> S >> M; // if (N == 1){ // cout << S << "\n"; // return; // } // mint ans = 0; // po167::Binomial table; // mint pro_sum = table.ruiseki(S, N); // vector f(M + 1); // rep(i, 0, (M + 2) / 2){ // f[i] = table.C(M, i); // f[i] *= table.fact(i); // } // reverse(all(f)); // vector g(M + 1); // rep(i, 0, M + 1){ // g[i] = table.invfact(i) * (i & 1 ? -1 : 1); // } // f = atcoder::convolution(f, g); // f.resize(M + 1); // rep(i, 0, M + 1) f[i] *= table.invfact(M - i); // mint inv = pro_sum.inv(); // mint tmp = 1; // vector X(S); // rep(i, 0, S){ // tmp -= table.ruiseki(S - i, N - 1) * inv; // X[i] = tmp; // } // auto Y = po167::Multipoint_Evaluation(f, X); // for (auto x : Y) ans += x; // ans *= N; // cout << ans.val() << "\n"; //} // #line 1 "g.cpp" #include using namespace std; using ll=long long; const ll ILL=2167167167167167167; const int INF=2100000000; #define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++) #define all(p) p.begin(),p.end() template using _pq = priority_queue, greater>; template int LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template int UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,T b){if(b bool chmax(T &a,T b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;} template void vec_out(vector &p,int ty=0){ if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'< T vec_min(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;} template T vec_max(vector &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;} template T vec_sum(vector &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;} int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;} template T square(T a){return a * a;} #line 2 "/Users/Shared/po167_library/fps/Multipoint_Evaluation.hpp" #include #line 4 "/Users/Shared/po167_library/fps/FPS_division.hpp" #line 4 "/Users/Shared/po167_library/fps/FPS_inv.hpp" namespace po167{ // return 1 / f template std::vector FPS_inv(std::vector f, int len = -1){ if (len == -1) len = f.size(); assert(f[0] != 0); std::vector g = {1 / f[0]}; int s = 1; while(s < len){ // g = 2g_s - f(g_s)^2 (mod x ^ (2 * s)) // g = g - (fg - 1)g // (fg - 1) = 0 (mod x ^ (s)) std::vector n_g(s * 2, 0); std::vector f_s(s * 2, 0); g.resize(s * 2); for (int i = 0; i < s * 2; i++){ if (int(f.size()) > i) f_s[i] = f[i]; n_g[i] = g[i]; } atcoder::internal::butterfly(g); atcoder::internal::butterfly(f_s); for (int i = 0; i < s * 2; i++){ f_s[i] *= g[i]; } atcoder::internal::butterfly_inv(f_s); T iz = 1 / (T)(s * 2); for (int i = s; i < s * 2; i++){ f_s[i] *= iz; } for (int i = 0; i < s; i++){ f_s[i] = 0; } atcoder::internal::butterfly(f_s); for (int i = 0; i < s * 2; i++){ f_s[i] *= g[i]; } atcoder::internal::butterfly_inv(f_s); for (int i = s; i < s * 2; i++){ n_g[i] -= f_s[i] * iz; } std::swap(n_g, g); s *= 2; } g.resize(len); return g; } } #line 6 "/Users/Shared/po167_library/fps/FPS_division.hpp" namespace po167{ template // f = g * res.first + res.second // |res.first| <= |f| - |g| + 1 // |res.second| <= |g| - 1 std::pair, std::vector> FPS_division(std::vector f, std::vector g){ while (!f.empty() && f.back() == 0) f.pop_back(); assert(!g.empty() && g.back() != 0); if (f.size() < g.size()){ return {{}, f}; } // rev(f) / rev(g) = rev(q) (mod x ^ {|f| - |g| + 1}) std::vector r = f; std::reverse(f.begin(), f.end()); std::reverse(g.begin(), g.end()); int z = (int)f.size() - (int)g.size() + 1; f.resize(z); std::vector q = atcoder::convolution(f, FPS_inv(g, z)); q.resize(z); std::reverse(g.begin(), g.end()); std::reverse(q.begin(), q.end()); f = atcoder::convolution(q, g); for (int i = 0; i < (int)f.size(); i++) r[i] -= f[i]; while (!q.empty() && q.back() == 0) q.pop_back(); while (!r.empty() && r.back() == 0) r.pop_back(); return {q, r}; } } #line 4 "/Users/Shared/po167_library/fps/Multipoint_Evaluation.hpp" namespace po167{ // return {f(p[0]), f(p[1]), f(p[2]), ... } template std::vector Multipoint_Evaluation( std::vector f, std::vector p ){ int m = p.size(); if (m == 0) return {}; if (m == 1){ T res = 0; T tmp = 1; for (auto x : f) res += tmp * x, tmp *= p[0]; return {res}; } int size = 1; while (size < m) size *= 2; std::vector> prod(size * 2); for (int i = 0; i < size; i++){ if (i < m) prod[i + size] = {(T)(-1) * p[i], 1}; else prod[i + size] = {1}; } for (int i = size - 1; i > 0; i--){ prod[i] = atcoder::convolution(prod[i * 2], prod[i * 2 + 1]); } std::vector res(m); auto calc = [&](auto self, int l, int r, int ind, std::vector tmp) -> void { if (m <= l) return; if (l + 1 == r){ res[l] = (tmp.empty() ? T(0) : tmp[0]); return; } int mid = (l + r) / 2; self(self, l, mid, ind * 2, po167::FPS_division(tmp, prod[ind * 2]).second); self(self, mid, r, ind * 2 + 1, po167::FPS_division(tmp, prod[ind * 2 + 1]).second); };calc(calc, 0, size, 1, f); return res; } } #line 2 "/Users/Shared/po167_library/math/Binomial.hpp" #line 5 "/Users/Shared/po167_library/math/Binomial.hpp" namespace po167{ template struct Binomial{ std::vector fact_vec, fact_inv_vec; void extend(int m = -1){ int n = fact_vec.size(); if (m == -1) m = n * 2; if (n >= m) return; fact_vec.resize(m); fact_inv_vec.resize(m); for (int i = n; i < m; i++){ fact_vec[i] = fact_vec[i - 1] * T(i); } fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1]; for (int i = m - 1; i > n; i--){ fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i); } } Binomial(int MAX = 0){ fact_vec.resize(1, T(1)); fact_inv_vec.resize(1, T(1)); extend(MAX + 1); } T fact(int i){ if (i < 0) return 0; while (int(fact_vec.size()) <= i) extend(); return fact_vec[i]; } T invfact(int i){ if (i < 0) return 0; while (int(fact_inv_vec.size()) <= i) extend(); return fact_inv_vec[i]; } T C(int a, int b){ if (a < b || b < 0) return 0; return fact(a) * invfact(b) * invfact(a - b); } T invC(int a, int b){ if (a < b || b < 0) return 0; return fact(b) * fact(a - b) *invfact(a); } T P(int a, int b){ if (a < b || b < 0) return 0; return fact(a) * invfact(a - b); } T inv(int a){ if (a < 0) return inv(-a) * T(-1); if (a == 0) return 1; return fact(a - 1) * invfact(a); } T Catalan(int n){ if (n < 0) return 0; return fact(2 * n) * invfact(n + 1) * invfact(n); } T narayana(int n, int k){ if (n <= 0 || n < k || k < 1) return 0; return C(n, k) * C(n, k - 1) * inv(n); } T Catalan_pow(int n,int d){ if (n < 0 || d < 0) return 0; if (d == 0){ if (n == 0) return 1; return 0; } return T(d) * inv(d + n) * C(2 * n + d - 1, n); } // retrun [x^a] 1/(1-x)^b T ruiseki(int a,int b){ if (a < 0 || b < 0) return 0; if (a == 0){ return 1; } return C(a + b - 1, b - 1); } // (a, b) -> (c, d) // always x + e >= y T mirror(int a, int b, int c, int d, int e = 0){ if (a + e < b || c + e < d) return 0; if (a > c || b > d) return 0; a += e; c += e; return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1); } // return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i) // return C(a + b + 2, a + 1) - 1; T gird_sum(int a, int b){ if (a < 0 || b < 0) return 0; return C(a + b + 2, a + 1) - 1; } // return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i) // AGC 018 E T gird_sum_2(int a, int b, int c, int d){ if (a >= b || c >= d) return 0; a--, b--, c--, d--; return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d); } // the number of diagonal dissections of a convex n-gon into k+1 regions. // OEIS A033282 // AGC065D T diagonal(int n, int k){ if (n <= 2 || n - 3 < k || k < 0) return 0; return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1); } }; } #line 27 "g.cpp" using mint = atcoder::modint998244353; void solve(); // POP'N ROLL MUSIC / TOMOO int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t = 1; // cin >> t; rep(i, 0, t) solve(); } void solve(){ int N, S, M; cin >> N >> S >> M; if (N == 1){ cout << S << "\n"; return; } mint ans = 0; po167::Binomial table; mint pro_sum = table.ruiseki(S, N); vector f(M + 1); rep(i, 0, (M + 2) / 2){ f[i] = table.C(M, i); f[i] *= table.fact(i); } reverse(all(f)); vector g(M + 1); rep(i, 0, M + 1){ g[i] = table.invfact(i) * (i & 1 ? -1 : 1); } f = atcoder::convolution(f, g); f.resize(M + 1); rep(i, 0, M + 1) f[i] *= table.invfact(M - i); mint inv = pro_sum.inv(); mint tmp = 1; vector X(S); rep(i, 0, S){ tmp -= table.ruiseki(S - i, N - 1) * inv; X[i] = tmp; } auto Y = po167::Multipoint_Evaluation(f, X); for (auto x : Y) ans += x; ans *= N; cout << ans.val() << "\n"; }