#define MD 998244353
ll@K,N=0,l=0;VVI v(2K+1);rep(K){ll@L,@M;N+=L*M;v[l++]={L,-M};v[l++]={M,-1};}v[l++]={N,1};sortV(v);mint a=1,f=a;K=1;rep[v](t,l){while(K<t[0])f*=++K;a*=f**(t[1]+MD-1);}wt(a);