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| #include<cstdio> #include<cstring> #include<algorithm> #include<iostream> #include<queue> #include<map> #include<stack> #include<cmath> #include<set> #include<bitset> #include<complex> #include<assert.h> #define inc(i,l,r) for(int i=l;i<=r;i++) #define dec(i,l,r) for(int i=l;i>=r;i--) #define link(x) for(edge *j=h[x];j;j=j->next) #define mem(a) memset(a,0,sizeof(a)) #define ll long long #define eps 1e-8 #define succ(x) (1<<x) #define lowbit(x) (x&(-x)) #define sqr(x) ((x)*(x)) #define mid (x+y)/2 #define NM 4005 #define nm 300005 using namespace std; const double pi=acos(-1); const ll inf=998244353; ll read(){ ll x=0,f=1;char ch=getchar(); while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();} while(isdigit(ch))x=x*10+ch-'0',ch=getchar(); return f*x; }
ll inv[NM],invp[NM],p[NM],l,_l,a[NM],b[NM],c[NM],d[NM],ans; int n,m; ll qpow(ll x,ll t){return t?qpow(sqr(x)%inf,t>>1)*(t&1?x:1ll)%inf:1ll;}
int main(){ n=read();m=read();l=read();_l=sqr(l)%inf; p[0]=p[1]=inv[1]=invp[0]=invp[1]=1; inc(i,2,n*2+1)p[i]=p[i-1]*i%inf,inv[i]=inv[inf%i]*(inf-inf/i)%inf,invp[i]=invp[i-1]*inv[i]%inf; a[0]=1; inc(k,1,n){ mem(b); inc(i,0,n)b[i+1]=-a[i]; inc(i,0,n)b[i]+=a[i]*_l%inf,b[i]%=inf; inc(i,0,n)a[i]=(b[i]+inf)%inf; if(k<m)continue; inc(i,0,n)c[i+n-k]+=b[i]*p[n]%inf*invp[k]%inf*invp[n-k]%inf,c[i+n-k]%=inf; } mem(a);a[0]=1;d[0]=c[0]; inc(k,1,n){ mem(b); inc(i,0,n*2)b[i]=a[i]*_l%inf; inc(i,0,n*2)b[i+1]+=inf-2*l%inf*a[i]%inf,b[i+1]%=inf; inc(i,0,n*2)b[i+2]+=2*a[i]%inf,b[i+2]%=inf; inc(i,0,n*2)a[i]=b[i]; inc(i,0,n*2)d[i]+=c[k]*a[i]%inf,d[i]%=inf; } for(int k=0,t=l;k<=2*n;k++,t=t*l%inf)ans+=d[k]*t%inf*inv[k+1]%inf,ans%=inf; ans*=qpow(qpow(_l,n),inf-2);ans%=inf;if(ans<0)ans+=inf; printf("%lld\n",ans); return 0; }
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