#include using namespace std; typedef signed long long ll; #define _P(...) (void)printf(__VA_ARGS__) #define FOR(x,to) for(x=0;x<(to);x++) #define FORR(x,arr) for(auto& x:arr) #define FORR2(x,y,arr) for(auto& [x,y]:arr) #define ALL(a) (a.begin()),(a.end()) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) template bool chmax(T &a, const T &b) { if(a bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;} //------------------------------------------------------- const int mo=998244353; ll modpow(ll a, ll n = mo-2) { ll r=1; a%=mo; while(n) r=r*((n%2)?a:1)%mo,a=a*a%mo,n>>=1; return r; } template using vec=vector; //using vec=valarray; template vec fft(vec v, bool rev=false) { int n=v.size(),i,j,m; for(int m=n; m>=2; m/=2) { T wn=modpow(5,(mo-1)/m); if(rev) wn=modpow(wn); for(i=0;i=mo) v[j1]-=mo; w=(ll)w*wn%mo; } } } for(i=0,j=1;j>1;k>(i^=k);k>>=1); if(i>j) swap(v[i],v[j]); } if(rev) { ll rv = modpow(n); FOR(i,n) v[i]=(ll)v[i]*rv%mo; } return v; } template vec MultPoly(vec P,vec Q,bool resize=false) { if(resize) { int maxind=0,pi=0,qi=0,i; int s=2; FOR(i,P.size()) if(norm(P[i])) pi=i; FOR(i,Q.size()) if(norm(Q[i])) qi=i; maxind=pi+qi+1; while(s*2 R(s*2); for(int x=0;x<=pi;x++) for(int y=0;y<=qi;y++) (R[x+y]+=P[x]*Q[y])%=mo; return R; } vec P2(s*2),Q2(s*2); FOR(i,pi+1) P2[i]=P[i]; FOR(i,qi+1) Q2[i]=Q[i]; swap(P,P2),swap(Q,Q2); } P=fft(P), Q=fft(Q); for(int i=0;i vector inverse(vector a) { assert(a[0]>0); vector b={(T)modpow(a[0])}; while(b.size() c(a.begin(),a.begin()+min(a.size(),2*b.size())); vector d=MultPoly(b,b,true); if(d.size()>a.size()) d.resize(a.size()); c = MultPoly(c,d,true); b.resize(2*b.size()); int i; for(i=b.size()/2;i exp_n(ll a,int N) { //exp(ax)をN次まで vector R={1}; int i; ll s=1; for(i=1;i<=N;i++) { s=s*a%mo; s=s*modpow(i)%mo; R.push_back(s); } return R; } ll comb(ll N_, ll C_) { const int NUM_=2400001; static ll fact[NUM_+1],factr[NUM_+1],inv[NUM_+1]; if (fact[0]==0) { inv[1]=fact[0]=factr[0]=1; for (int i=2;i<=NUM_;++i) inv[i] = inv[mo % i] * (mo - mo / i) % mo; for (int i=1;i<=NUM_;++i) fact[i]=fact[i-1]*i%mo, factr[i]=factr[i-1]*inv[i]%mo; } if(C_<0 || C_>N_) return 0; return factr[C_]*fact[N_]%mo*factr[N_-C_]%mo; } int H,W,N,K; void solve() { int i,j,k,l,r,x,y; string s; vector fact(1505050); fact[0]=1; for(i=1;i<=1501010;i++) fact[i]=fact[i-1]*i%mo; cin>>H>>W>>N>>K; int numH=0,Hma=0;; int numW=0,Wma=0;; if(2*K<=H) { numH=K-1; Hma=H-2*K+2; } else { numH=H-K; Hma=2*K-H; } if(2*K<=W) { numW=K-1; Wma=W-2*K+2; } else { numW=W-K; Wma=2*K-W; } vector E=exp_n(1,N+2); vector EH=exp_n(numH+1,N+2); vector EW=exp_n(numW+1,N+2); reverse(ALL(E)); reverse(ALL(EH)); reverse(ALL(EW)); E.pop_back(); EH.pop_back(); EW.pop_back(); reverse(ALL(E)); reverse(ALL(EH)); reverse(ALL(EW)); E=inverse(E); EH=MultPoly(E,EH,1); EW=MultPoly(E,EW,1); EH[0]--; EW[0]--; ll s0=numH*2+Hma,s1=numW*2+Wma; ll ret=(s0%mo)*(s1%mo)%mo; ll rL=mo-modpow(1LL*(H-K+1)*(W-K+1)); ll rLP=1; FOR(i,N+1) { ll Hs=(2*EH[i]*fact[i]%mo+1LL*Hma*modpow(numH+1,i))%mo; ll Ws=(2*EW[i]*fact[i]%mo+1LL*Wma*modpow(numW+1,i))%mo; ret-=comb(N,i)*rLP%mo*Hs%mo*Ws%mo; rLP=rLP*rL%mo; } ret=(ret%mo+mo)%mo; cout<