#include using namespace std; #define ALL(x) begin(x),end(x) #define rep(i,n) for(int i=0;i<(n);i++) #define debug(v) cout<<#v<<":";for(auto x:v){cout<bool chmax(T &a,const T &b){if(abool chmin(T &a,const T &b){if(b ostream &operator<<(ostream &os,const vector&v){ for(int i=0;i<(int)v.size();i++) os< istream &operator>>(istream &is,vector&v){ for(T &x:v)is>>x; return is; } template struct ModInt{ long long x; ModInt():x(0){} ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%Mod){} ModInt &operator+=(const ModInt &p){ if((x+=p.x)>=Mod) x-=Mod; return *this; } ModInt &operator-=(const ModInt &p){ if((x+=Mod-p.x)>=Mod)x-=Mod; return *this; } ModInt &operator*=(const ModInt &p){ x=(int)(1ll*x*p.x%Mod); return *this; } ModInt &operator/=(const ModInt &p){ (*this)*=p.inverse(); return *this; } ModInt operator-()const{return ModInt(-x);} ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;} ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;} ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;} ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;} bool operator==(const ModInt &p)const{return x==p.x;} bool operator!=(const ModInt &p)const{return x!=p.x;} ModInt inverse()const{ int a=x,b=Mod,u=1,v=0,t; while(b>0){ t=a/b; swap(a-=t*b,b);swap(u-=t*v,v); } return ModInt(u); } ModInt pow(long long n)const{ ModInt ret(1),mul(x); while(n>0){ if(n&1) ret*=mul; mul*=mul;n>>=1; } return ret; } friend ostream &operator<<(ostream &os,const ModInt &p){return os<>(istream &is,ModInt &a){long long t;is>>t;a=ModInt(t);return (is);} static int get_mod(){return Mod;} }; template struct Precalc{ vector fact,finv,inv; int Mod; Precalc(int MX):fact(MX),finv(MX),inv(MX),Mod(T::get_mod()){ fact[0]=T(1),fact[1]=T(1),finv[0]=T(1),finv[1]=T(1),inv[1]=T(1); for(int i=2;i> partition_function_table(int n,int k){ vector> ret(n+1,vector(k+1,0)); ret[0][0]=1; for(int i=0;i<=n;i++)for(int j=1;j<=k;j++)if(i or j){ ret[i][j]=ret[i][j-1]; if(i-j>=0) ret[i][j]+=ret[i-j][j]; } return ret; } // n = y.size - 1 // n次の多項式f, f(0), f(k)の値がわかっていればf(t)が求まる // 1^k + ... n^k はk+1次多項式,k=1ならn(n+1)/2 T LagrangePolynomial(vector y,long long t){ int n=(int)y.size()-1; if(t<=n) return y[t]; T ret=T(0); vector l(n+1,1),r(n+1,1); for(int i=0;i0;i--) r[i-1]=r[i]*(t-i); for(int i=0;i<=n;i++){ T add=y[i]*l[i]*r[i]*finv[i]*finv[n-i]; ret+=((n-i)%2?-add:add); } return ret; } /* sum combination(n+x, x), x=l to r https://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=ja check n+x < [COM_PRECALC_MAX] */ T sum_of_comb(int n,int l,int r){ if(l>r)return T(0); T ret=T(r+1)*com(n+r+1,r+1)-T(l)*com(l+n,l); ret/=T(n+1); return ret; } /* - sum of comb 2 https://www.wolframalpha.com/input/?i=sum+combination%28i%2Bj%2Ci%29%2C+i%3D0+to+a-1%2C+j%3D0+to+b-1&lang=ja https://yukicoder.me/problems/no/1489 sum binom(i+j,i) i=0 to a-1, j=0 to b-1 = ( binom(a+b,a-1)*(b+1)/a ) - 1 */ }; template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { vector< Mint > dw, idw; int max_base; Mint root; NumberTheoreticTransformFriendlyModInt() { const unsigned mod = Mint::get_mod(); assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(root.pow((mod - 1) >> 1) == 1) root += 1; assert(root.pow(mod - 1) == 1); dw.resize(max_base); idw.resize(max_base); for(int i = 0; i < max_base; i++) { dw[i] = -root.pow((mod - 1) >> (i + 2)); idw[i] = Mint(1) / dw[i]; } } void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = n; m >>= 1;) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; a[i] = x + y, a[j] = x - y; } w *= dw[__builtin_ctz(++k)]; } } } void intt(vector< Mint > &a, bool f = true) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = 1; m < n; m *= 2) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * w; } w *= idw[__builtin_ctz(++k)]; } } if(f) { Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } } vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); return a; } }; using mint=ModInt<998244353>; using P=pair; Precalc F(3000100); NumberTheoreticTransformFriendlyModInt ntt; bool between(P a,P b,P c){ return a.first<=b.first and b.first<=c.first and a.second<=b.second and b.second<=c.second; } bool ord(P a,P b){ return a.first<=b.first and a.second<=b.second; } mint way(P a,P b){ if(!ord(a,b)) return mint(0); return F.com(b.first-a.first+b.second-a.second,b.first-a.first); } vector multiply(vector &a,vector &b){ vector ret(a.size()+b.size()-1,0); rep(i,a.size())rep(j,b.size()) ret[i+j]+=a[i]*b[j]; return ret; } void shift(vector &v){ v.push_back(v.back()); for(int i=v.size()-1;i>=0;i--) v[i+1]=v[i]; v[0]=0; return ; } // vecs[0] is result void merge_ntt(vector> &vecs){ int N=(int)vecs.size(); priority_queue,vector>,greater>> que; rep(i,N) que.emplace(vecs[i].size(),i); while(que.size()>1){ int i=que.top().second;que.pop(); int j=que.top().second;que.pop(); if(i>j) swap(i,j); vecs[i]=ntt.multiply(vecs[i],vecs[j]); que.emplace(vecs[i].size(),i); } } signed main(){ int N,M,L,K;cin>>N>>M>>L>>K; vector

C,T; C.emplace_back(0,0); rep(i,M){ int x,y;cin>>x>>y; C.emplace_back(x,y); } C.emplace_back(N,N); rep(i,L){ int x,y;cin>>x>>y; T.emplace_back(x,y); if(x==0 and y==0) K--; } vector> TS(C.size()); vector> pool; rep(i,(int)C.size()-1)rep(j,L) if(between(C[i],T[j],C[i+1]) and T[j]!=C[i]) TS[i].push_back(T[j]); vector ans(1,1); rep(i,(int)C.size()-1){ auto &W=TS[i]; sort(ALL(W)); vector> dp(W.size(),vector(W.size()+2,0)); for(int j=0;j0;k--){ dp[j][k]-=S; S+=dp[j][k]; } } vector res(W.size()+2,0); if(W.empty() or W.back()!=C[i+1]) res[0]=way(C[i],C[i+1]); for(int j=0;j=(W.back()==C[i+1]);k--){ res[k]-=S; S+=res[k]; } } pool.push_back(move(res)); } merge_ntt(pool); mint sum=0; for(int i=0;i<=K and i