#include #include #include using namespace atcoder; using mint = modint998244353; using namespace std; #define rep(i,n) for (int i = 0; i < (n); ++i) #define Inf32 1000000001 #define Inf64 3000000000000000 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(){ combi c(100000); int C,X; cin>>C>>X; vector dp(X+1,vector(2,0)); dp[0][0] =1; for(int i=1;i<=100000;i++){ int l = 0; int r = C+i-1; mint len = r-l+1; len = len.inv(); if(r>X)break; vector ndp(X+1,vector(2,0)); rep(j,X+1){ { mint p = j; p *= len; ndp[j][0] += dp[j][0] * p; } if(j!=X){ mint p = min(r-l+1,X)-j; p *= len; ndp[j+1][0] += dp[j][0] * p; } if(r==X){ mint p = 1; p *= len; ndp[j][1] += dp[j][0]*p; } } swap(dp,ndp); } mint ans = 0; rep(i,X){ rep(j,2){ //cout<<(dp[i][j]*6).val()<<','; if(j==0){ int r = X-i; mint p = c.kaijou[r]; p *= c.kaijou_[r+1]; ans += dp[i][j] * (1-p); } else{ ans += dp[i][j]; } } //cout<