// g++-14 1.cpp -std=c++20 -O2 -I . #include using namespace std; #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include using namespace __gnu_pbds; #include #include using namespace atcoder; using ll = long long; using ld = long double; using vi = vector; using vvi = vector; using vll = vector; using vvll = vector; using vld = vector; using vvld = vector; using vst = vector; using vvst = vector; #define fi first #define se second #define pb push_back #define eb emplace_back #define pq_big(T) priority_queue,less> #define pq_small(T) priority_queue,greater> #define all(a) a.begin(),a.end() #define rep(i,start,end) for(ll i=start;i<(ll)(end);i++) #define per(i,start,end) for(ll i=start;i>=(ll)(end);i--) #define uniq(a) sort(all(a));a.erase(unique(all(a)),a.end()) random_device seed; mt19937_64 randint(seed()); ll grr(ll mi, ll ma) { // [mi, ma) return mi + randint() % (ma - mi); } using mint = modint998244353; using fps = vector; const int MAX=510000; const long long MOD=998244353; long long fac[MAX],finv[MAX],inv[MAX]; void COMinit(){ fac[0]=fac[1]=1; finv[0]=finv[1]=1; inv[1]=1; for(int i=2;i=0); fps res(1); res[0]=1/f[0]; for(int m=1;m div_fps(fps &f,fps g){ while(!g.empty()&&g.back().val()==0){ g.pop_back(); } if(g.empty()){ cerr<<"ERROR : g is 0"< multipoint_evalution(fps &f,vector &x){ int m=x.size(); int d=0; while((1< tree1(2*n),tree2(2*n); rep(i,0,n){ if(i res; rep(i,0,m){ if(tree2[n+i].size()==0){ res.emplace_back(0); } else{ res.emplace_back(tree2[n+i][0].val()); } } return res; } // f(x) の係数が与えられて f(x+c) を x の多項式として展開する // https://judge.yosupo.jp/submission/283667 fps taylor_shift(fps &f,ll c){ if(c==0)return f; int n=f.size(); fps f2=f; rep(i,0,n)f2[i]*=fac[i]; reverse(all(f2)); fps expcx(n,1); mint cs=c; rep(i,1,n){ expcx[i]=cs*finv[i]; cs*=c; } f2=convolution(f2,expcx); while(f2.size()>n)f2.pop_back(); reverse(all(f2)); rep(i,0,n){ f2[i]*=finv[i]; } return f2; } // sum i = [0, n]: a_i (x + p)^i (x + q)^(n - i) // a の長さは n + 1 を要求 fps sub(int n,vector &a,mint p,mint q){ fps f(n+1); mint c=1; rep(i,0,n+1){ f[i]=c*a[i]; c*=p-q; } f=taylor_shift(f,((mint)1/(p-q)).val()); reverse(all(f)); f=taylor_shift(f,q.val()); return f; } int main(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); COMinit(); int n,s,m;cin>>n>>s>>m; vector ps; rep(i,1,s+1){ mint prob=fac[s]*fac[n+s-i-1]; prob*=finv[s-i]*finv[n+s-1]; ps.emplace_back(prob); } vector a(m+1,0); rep(i,(m+1)/2,m+1){ a[i]=COM(m,i); if((m-i)%2==1)a[i]*=-1; } fps f=sub(m,a,0,-1); vector evals=multipoint_evalution(f,ps); mint ans=0; for(mint e:evals){ ans+=e; } ans*=n; cout<