#pragma GCC optimize ("Ofast") #include using namespace std; #define MD (998244353U) void*wmem; char memarr[96000000]; template inline S min_L(S a,T b){ return a<=b?a:b; } template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } template inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){ walloc1d(arr, x2-x1, mem); (*arr) -= x1; } template void sortA_L(int N, T1 a[], void *mem = wmem){ sort(a, a+N); } template void sortA_L(int N, T1 a[], T2 b[], void *mem = wmem){ int i; pair*arr; walloc1d(&arr, N, &mem); for(i=(0);i<(N);i++){ arr[i].first = a[i]; arr[i].second = b[i]; } sort(arr, arr+N); for(i=(0);i<(N);i++){ a[i] = arr[i].first; b[i] = arr[i].second; } } struct Modint{ unsigned val; Modint(){ val=0; } Modint(int a){ val = ord(a); } Modint(unsigned a){ val = ord(a); } Modint(long long a){ val = ord(a); } Modint(unsigned long long a){ val = ord(a); } inline unsigned ord(unsigned a){ return a%MD; } inline unsigned ord(int a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned ord(unsigned long long a){ return a%MD; } inline unsigned ord(long long a){ a %= (int)MD; if(a < 0){ a += MD; } return a; } inline unsigned get(){ return val; } inline Modint &operator+=(Modint a){ val += a.val; if(val >= MD){ val -= MD; } return *this; } inline Modint &operator-=(Modint a){ if(val < a.val){ val = val + MD - a.val; } else{ val -= a.val; } return *this; } inline Modint &operator*=(Modint a){ val = ((unsigned long long)val*a.val)%MD; return *this; } inline Modint &operator/=(Modint a){ return *this *= a.inverse(); } inline Modint operator+(Modint a){ return Modint(*this)+=a; } inline Modint operator-(Modint a){ return Modint(*this)-=a; } inline Modint operator*(Modint a){ return Modint(*this)*=a; } inline Modint operator/(Modint a){ return Modint(*this)/=a; } inline Modint operator+(int a){ return Modint(*this)+=Modint(a); } inline Modint operator-(int a){ return Modint(*this)-=Modint(a); } inline Modint operator*(int a){ return Modint(*this)*=Modint(a); } inline Modint operator/(int a){ return Modint(*this)/=Modint(a); } inline Modint operator+(long long a){ return Modint(*this)+=Modint(a); } inline Modint operator-(long long a){ return Modint(*this)-=Modint(a); } inline Modint operator*(long long a){ return Modint(*this)*=Modint(a); } inline Modint operator/(long long a){ return Modint(*this)/=Modint(a); } inline Modint operator-(void){ Modint res; if(val){ res.val=MD-val; } else{ res.val=0; } return res; } inline operator bool(void){ return val!=0; } inline operator int(void){ return get(); } inline operator long long(void){ return get(); } inline Modint inverse(){ int a = val; int b = MD; int u = 1; int v = 0; int t; Modint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += MD; } res.val = u; return res; } inline Modint pw(unsigned long long b){ Modint a(*this); Modint res; res.val = 1; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } inline bool operator==(int a){ return ord(a)==val; } inline bool operator!=(int a){ return ord(a)!=val; } } ; inline Modint operator+(int a, Modint b){ return Modint(a)+=b; } inline Modint operator-(int a, Modint b){ return Modint(a)-=b; } inline Modint operator*(int a, Modint b){ return Modint(a)*=b; } inline Modint operator/(int a, Modint b){ return Modint(a)/=b; } inline Modint operator+(long long a, Modint b){ return Modint(a)+=b; } inline Modint operator-(long long a, Modint b){ return Modint(a)-=b; } inline Modint operator*(long long a, Modint b){ return Modint(a)*=b; } inline Modint operator/(long long a, Modint b){ return Modint(a)/=b; } inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(Modint x){ int i; i = (int)x; wt_L(i); } template inline void arrInsert(const int k, int &sz, S a[], const S aval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } a[k] = aval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } a[k] = aval; b[k] = bval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } for(i=sz-1;i>k;i--){ c[i] = c[i-1]; } a[k] = aval; b[k] = bval; c[k] = cval; } template inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval, V d[], const V dval){ int i; sz++; for(i=sz-1;i>k;i--){ a[i] = a[i-1]; } for(i=sz-1;i>k;i--){ b[i] = b[i-1]; } for(i=sz-1;i>k;i--){ c[i] = c[i-1]; } for(i=sz-1;i>k;i--){ d[i] = d[i-1]; } a[k] = aval; b[k] = bval; c[k] = cval; d[k] = dval; } template inline S chmax(S &a, T b){ if(a struct Comb{ int mem_fact; T*factri; T*ifactri; int mem_dfact; T*dfactri; int mem_pw2; int mem_pw3; int mem_pw10; int mem_rep1; T*pw2c; T*pw3c; T*pw10c; T*rep1c; int mem_ipw2; int mem_ipw3; int mem_ipw10; T*ipw2c; T*ipw3c; T*ipw10c; Comb(){ mem_fact = 0; mem_dfact = 0; mem_pw2 = mem_pw3 = mem_pw10 = mem_rep1 = 0; mem_ipw2 = mem_ipw3 = mem_ipw10 = 0; } inline void expand_fact(int k){ int i; if(k <= mem_fact){ return; } chmax(k, 2 * mem_fact); if(mem_fact == 0){ factri = (T*)malloc(k * sizeof(T)); ifactri = (T*)malloc(k * sizeof(T)); factri[0] = 1; for(i=(1);i<(k);i++){ factri[i] = i * factri[i-1]; } ifactri[k-1] = 1 / factri[k-1]; for(i=(k-1)-1;i>=(0);i--){ ifactri[i] = (i+1) * ifactri[i+1]; } } else{ factri = (T*)realloc(factri, k * sizeof(T)); ifactri = (T*)realloc(ifactri, k * sizeof(T)); for(i=(mem_fact);i<(k);i++){ factri[i] = i * factri[i-1]; } ifactri[k-1] = 1 / factri[k-1]; for(i=(k-1)-1;i>=(mem_fact);i--){ ifactri[i] = (i+1) * ifactri[i+1]; } } mem_fact = k; } inline T fac(int k){ if(mem_fact < k+1){ expand_fact(k+1); } return factri[k]; } inline T ifac(int k){ if(mem_fact < k+1){ expand_fact(k+1); } return ifactri[k]; } inline T C(int a, int b){ if(b < 0 || b > a){ return 0; } if(mem_fact < a+1){ expand_fact(a+1); } return factri[a] * ifactri[b] * ifactri[a-b]; } inline T P(int a, int b){ if(b < 0 || b > a){ return 0; } if(mem_fact < a+1){ expand_fact(a+1); } return factri[a] * ifactri[a-b]; } inline T H(int a, int b){ if(a==0 && b==0){ return 1; } if(a <= 0 || b < 0){ return 0; } if(mem_fact < a+b){ expand_fact(a+b); } return C(a+b-1, b); } inline T Multinomial(int sz, int a[]){ int i; int s = 0; T res; for(i=(0);i<(sz);i++){ s += a[i]; } if(mem_fact < s+1){ expand_fact(s+1); } res = factri[s]; for(i=(0);i<(sz);i++){ res *= ifactri[a[i]]; } return 1; } inline T Multinomial(int a){ return 1; } inline T Multinomial(int a, int b){ if(mem_fact < a+b+1){ expand_fact(a+b+1); } return factri[a+b] * ifactri[a] * ifactri[b]; } inline T Multinomial(int a, int b, int c){ if(mem_fact < a+b+c+1){ expand_fact(a+b+c+1); } return factri[a+b+c] * ifactri[a] * ifactri[b] * ifactri[c]; } inline T Multinomial(int a, int b, int c, int d){ if(mem_fact < a+b+c+d+1){ expand_fact(a+b+c+d+1); } return factri[a+b+c+d] * ifactri[a] * ifactri[b] * ifactri[c] * ifactri[d]; } inline T Catalan(int n){ if(n < 0){ return 0; } if(mem_fact < 2*n+1){ expand_fact(2*n+1); } return factri[2*n] * ifactri[n] * ifactri[n+1]; } inline T C_s(long long a, long long b){ long long i; T res; if(b < 0 || b > a){ return 0; } if(b > a - b){ b = a - b; } res = 1; for(i=(0);i<(b);i++){ res *= a - i; res /= i + 1; } return res; } inline T P_s(long long a, long long b){ long long i; T res; if(b < 0 || b > a){ return 0; } res = 1; for(i=(0);i<(b);i++){ res *= a - i; } return res; } inline T per_s(long long n, long long k){ T d; int m; if(n < 0 || k < 0){ return 0; } if(n == k && k == 0){ return 1; } if(n == 0 || k == 0){ return 0; } if(k==1){ return 1; } if(k==2){ d = n / 2; return d; } if(k==3){ d = (n-1) / 6; m = (n-1) % 6; if(m==0){ return 3 * d * d + d; } if(m==1){ return 3 * d * d + 2 * d; } if(m==2){ return 3 * d * d + 3 * d + 1; } if(m==3){ return 3 * d * d + 4 * d + 1; } if(m==4){ return 3 * d * d + 5 * d + 2; } if(m==5){ return 3 * d * d + 6 * d + 3; } } assert(0 && "per_s should be k <= 3"); return -1; } inline void expand_dfact(int k){ int i; if(k <= mem_dfact){ return; } chmax(k, 3); chmax(k, 2 * mem_dfact); if(mem_dfact==0){ dfactri = (T*)malloc(k * sizeof(T)); dfactri[0] = dfactri[1] = 1; for(i=(2);i<(k);i++){ dfactri[i] = i * dfactri[i-2]; } } else{ dfactri = (T*)realloc(dfactri, k * sizeof(T)); for(i=(mem_dfact);i<(k);i++){ dfactri[i] = i * dfactri[i-2]; } } mem_dfact = k; } inline void expand_pw2(int k){ int i; if(k <= mem_pw2){ return; } chmax(k, 2 * mem_pw2); if(mem_pw2==0){ pw2c = (T*)malloc(k * sizeof(T)); pw2c[0] = 1; for(i=(1);i<(k);i++){ pw2c[i] = 2 * pw2c[i-1]; } } else{ pw2c = (T*)realloc(pw2c, k * sizeof(T)); for(i=(mem_pw2);i<(k);i++){ pw2c[i] = 2 * pw2c[i-1]; } } mem_pw2 = k; } inline void expand_ipw2(int k){ int i; if(k <= mem_ipw2){ return; } chmax(k, 2); chmax(k, 2 * mem_ipw2); if(mem_ipw2==0){ ipw2c = (T*)malloc(k * sizeof(T)); ipw2c[0] = 1; ipw2c[1] = ipw2c[0] / 2; for(i=(1);i<(k);i++){ ipw2c[i] = ipw2c[1] * ipw2c[i-1]; } } else{ ipw2c = (T*)realloc(ipw2c, k * sizeof(T)); for(i=(mem_ipw2);i<(k);i++){ ipw2c[i] = ipw2c[1] * ipw2c[i-1]; } } mem_ipw2 = k; } inline void expand_pw3(int k){ int i; if(k <= mem_pw3){ return; } chmax(k, 2 * mem_pw3); if(mem_pw3==0){ pw3c = (T*)malloc(k * sizeof(T)); pw3c[0] = 1; for(i=(1);i<(k);i++){ pw3c[i] = 3 * pw3c[i-1]; } } else{ pw3c = (T*)realloc(pw3c, k * sizeof(T)); for(i=(mem_pw3);i<(k);i++){ pw3c[i] = 3 * pw3c[i-1]; } } mem_pw3 = k; } inline void expand_ipw3(int k){ int i; if(k <= mem_ipw3){ return; } chmax(k, 2); chmax(k, 2 * mem_ipw3); if(mem_ipw3==0){ ipw3c = (T*)malloc(k * sizeof(T)); ipw3c[0] = 1; ipw3c[1] = ipw3c[0] / 3; for(i=(1);i<(k);i++){ ipw3c[i] = ipw3c[1] * ipw3c[i-1]; } } else{ ipw3c = (T*)realloc(ipw3c, k * sizeof(T)); for(i=(mem_ipw3);i<(k);i++){ ipw3c[i] = ipw3c[1] * ipw3c[i-1]; } } mem_ipw3 = k; } inline void expand_pw10(int k){ int i; if(k <= mem_pw10){ return; } chmax(k, 2 * mem_pw10); if(mem_pw10==0){ pw10c = (T*)malloc(k * sizeof(T)); pw10c[0] = 1; for(i=(1);i<(k);i++){ pw10c[i] = 10 * pw10c[i-1]; } } else{ pw10c = (T*)realloc(pw10c, k * sizeof(T)); for(i=(mem_pw10);i<(k);i++){ pw10c[i] = 10 * pw10c[i-1]; } } mem_pw10 = k; } inline void expand_ipw10(int k){ int i; if(k <= mem_ipw10){ return; } chmax(k, 2); chmax(k, 2 * mem_ipw10); if(mem_ipw10==0){ ipw10c = (T*)malloc(k * sizeof(T)); ipw10c[0] = 1; ipw10c[1] = ipw10c[0] / 10; for(i=(1);i<(k);i++){ ipw10c[i] = ipw10c[1] * ipw10c[i-1]; } } else{ ipw10c = (T*)realloc(ipw10c, k * sizeof(T)); for(i=(mem_ipw10);i<(k);i++){ ipw10c[i] = ipw10c[1] * ipw10c[i-1]; } } mem_ipw10 = k; } inline void expand_rep1(int k){ int i; if(k <= mem_rep1){ return; } chmax(k, 2 * mem_rep1); if(mem_rep1==0){ rep1c = (T*)malloc(k * sizeof(T)); rep1c[0] = 0; for(i=(1);i<(k);i++){ rep1c[i] = 10 * rep1c[i-1] + 1; } } else{ rep1c = (T*)realloc(rep1c, k * sizeof(T)); for(i=(mem_rep1);i<(k);i++){ rep1c[i] = 10 * rep1c[i-1] + 1; } } mem_rep1 = k; } inline T dfac(int k){ if(k >= 0){ if(mem_dfact < k+1){ expand_dfact(k+1); } return dfactri[k]; } if(k==-1){ return 1; } k = - k - 2; if(k % 4 == 1){ return 1 / (-dfac(k)); } return 1 / dfac(k); } inline T pw2(int k){ if(k >= 0){ if(mem_pw2 < k+1){ expand_pw2(k+1); } return pw2c[k]; } else{ k = -k; if(mem_ipw2 < k+1){ expand_ipw2(k+1); } return ipw2c[k]; } } inline T pw3(int k){ if(k >= 0){ if(mem_pw3 < k+1){ expand_pw3(k+1); } return pw3c[k]; } else{ k = -k; if(mem_ipw3 < k+1){ expand_ipw3(k+1); } return ipw3c[k]; } } inline T pw10(int k){ if(k >= 0){ if(mem_pw10 < k+1){ expand_pw10(k+1); } return pw10c[k]; } else{ k = -k; if(mem_ipw10 < k+1){ expand_ipw10(k+1); } return ipw10c[k]; } } inline T repunit(int k){ if(mem_rep1 < k+1){ expand_rep1(k+1); } return rep1c[k]; } } ; template<> inline Modint Comb::C_s(long long a, long long b){ long long i; Modint res; Modint d; if(b < 0 || b > a){ return 0; } if(b > a - b){ b = a - b; } res = d = 1; for(i=(0);i<(b);i++){ res *= a - i; d *= i + 1; } return res / d; } int N; int M; int L; int K; int X[200000+2]; int Y[200000+2]; int XT[100]; int YT[100]; int tx[102]; int ty[102]; int ts; int ad; Modint dp[101]; Modint nx[101]; Modint ps[102][103]; int main(){ int i, k; wmem = memarr; Modint res = 0; Comb c; rd(N); rd(M); rd(L); rd(K); M += 2; for(i=(1);i<(M-1);i++){ rd(X[i]); rd(Y[i]); } X[M-1] = Y[M-1] = N; { int Q5VJL1cS; for(Q5VJL1cS=(0);Q5VJL1cS<(L);Q5VJL1cS++){ rd(XT[Q5VJL1cS]); rd(YT[Q5VJL1cS]); } } sortA_L(L, XT, YT); dp[0] = 1; for(k=(1);k<(M);k++){ int j; ts = ad = 0; arrInsert(ts, ts, tx, X[k-1], ty, Y[k-1]); for(i=(0);i<(L);i++){ if(XT[i] < X[k-1] || YT[i] < Y[k-1]){ continue; } if(XT[i] > X[k] || YT[i] > Y[k]){ continue; } if(XT[i] == X[k-1] && YT[i] == Y[k-1]){ ad++; continue; } if(XT[i] == X[k] && YT[i] == Y[k]){ continue; } arrInsert(ts, ts, tx, XT[i], ty, YT[i]); } arrInsert(ts, ts, tx, X[k], ty, Y[k]); for(i=(0);i<(ts);i++){ int j; for(j=(0);j<(ts);j++){ ps[i][j] = 0; } } ps[0][0] = 1; for(i=(0);i<(ts);i++){ int j; for(j=(0);j<(ts);j++){ if(ps[i][j]){ int m; for(m=(i+1);m<(ts);m++){ ps[m][j+1] += ps[i][j] * c.C(tx[m]-tx[i] + ty[m]-ty[i], tx[m]-tx[i]); } } } } for(j=(ts)-1;j>=(1);j--){ int m; for(m=(j+1);m<(ts);m++){ ps[ts-1][j] -= ps[ts-1][m] * c.C(m-1, j-1); } } for(i=(0);i<(L+1);i++){ nx[i] = 0; } for(i=(0);i<(L+1);i++){ if(dp[i]){ for(j=(1);j<(ts);j++){ nx[i+j+ad-1] += dp[i] * ps[ts-1][j]; } } } for(i=(0);i<(L+1);i++){ dp[i] = nx[i]; } } for(i=(0);i<(min_L(L, K)+1);i++){ res += dp[i]; } wt_L(res); wt_L('\n'); return 0; } // cLay version 20210103-1 [bug fixed 1] // --- original code --- // #define MD 998244353 // int N, M, L, K; // int X[2d5+2], Y[2d5+2], XT[100], YT[100]; // int tx[102], ty[102], ts, ad; // Modint dp[101], nx[101], ps[102][103]; // { // Modint res = 0; // Comb c; // rd(N,M,L,K); // M += 2; // rep(i,1,M-1) rd(X[i], Y[i]); // X[M-1] = Y[M-1] = N; // rd((XT, YT)(L)); // sortA(L, XT, YT); // // dp[0] = 1; // rep(k,1,M){ // ts = ad = 0; // arrInsert(ts, ts, tx, X[k-1], ty, Y[k-1]); // rep(i,L){ // if(XT[i] < X[k-1] || YT[i] < Y[k-1]) continue; // if(XT[i] > X[k] || YT[i] > Y[k]) continue; // if(XT[i] == X[k-1] && YT[i] == Y[k-1]) ad++, continue; // if(XT[i] == X[k] && YT[i] == Y[k]) continue; // arrInsert(ts, ts, tx, XT[i], ty, YT[i]); // } // arrInsert(ts, ts, tx, X[k], ty, Y[k]); // // rep(i,ts) rep(j,ts) ps[i][j] = 0; // ps[0][0] = 1; // rep(i,ts) rep(j,ts) if(ps[i][j]) rep(m,i+1,ts){ // ps[m][j+1] += ps[i][j] * c.C(tx[m]-tx[i] + ty[m]-ty[i], tx[m]-tx[i]); // } // rrep(j,1,ts) rep(m,j+1,ts) ps[ts-1][j] -= ps[ts-1][m] * c.C(m-1, j-1); // rep(i,L+1) nx[i] = 0; // rep(i,L+1) if(dp[i]) rep(j,1,ts) nx[i+j+ad-1] += dp[i] * ps[ts-1][j]; // rep(i,L+1) dp[i] = nx[i]; // } // // rep(i,min(L,K)+1) res += dp[i]; // wt(res); // }