#include #include #include using namespace atcoder; using mint = modint998244353; using namespace std; #define rep(i,n) for (int i = 0; i < (n); ++i) #define Inf 1000000001 struct combi{ deque kaijou; deque kaijou_; combi(int n){ kaijou.push_back(1); for(int i=1;i<=n;i++){ kaijou.push_back(kaijou[i-1]*i); } mint b=kaijou[n].inv(); kaijou_.push_front(b); for(int i=1;i<=n;i++){ int k=n+1-i; kaijou_.push_front(kaijou_[0]*k); } } mint combination(int n,int r){ if(r>n)return 0; mint a = kaijou[n]*kaijou_[r]; a *= kaijou_[n-r]; return a; } mint junretsu(int a,int b){ mint x = kaijou_[a]*kaijou_[b]; x *= kaijou[a+b]; return x; } mint catalan(int n){ return combination(2*n,n)/(n+1); } }; int main(){ int N,M,K; cin>>N>>M>>K; mint ans = 0; combi C(500000); if(M==0&&K==0){ ans = C.kaijou[N]; } else if(M+K>=N){ int r = M+K; r -= N; M -= r; K -= r; rep(i,min(M,K)+1){ ans += C.combination(M,i) * C.combination(K,i) * C.kaijou[i]; } } else{ vector dp(N+1,vector(2,0)); dp[0][0] = 1; rep(i,N){ rep(j,2){ dp[i+1][0] += dp[i][j]; dp[i+1][1] += dp[i][j] * (i+1); } } vector a(N+1,0),b(N+1,0); rep(i,min(M,K)+1){ int num = M+K; num -= i; mint v = C.combination(M,i); v *= C.combination(K,i); v *= C.kaijou[i]; num--; num+=i; v *= C.kaijou_[num]; a[num] += v; //cout<