//@formatter:off #include #define overload4(_1,_2,_3,_4,name,...) name #define rep1(i,n) for (ll i = 0; i < ll(n); ++i) #define rep2(i,s,n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i,s,n,d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep(i,n) for (ll i = ll(n)-1; i >= 0; i--) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define pb push_back #define eb emplace_back #define vi vector #define vvi vector> #define vl vector #define vvl vector> #define vd vector #define vvd vector> #define vs vector #define vc vector #define vvc vector> #define vb vector #define vvb vector> #define vp vector

#define vvp vector> #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0) #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using ll = long long; using P = pair; using LP = pair; template istream& operator>>(istream &is,pair &p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream &os,const pair &p) { return os<<'{'< istream& operator>>(istream &is,vector &v) { for(T &t:v){is>>t;} return is; } template ostream& operator<<(ostream &os,const vector &v) { os<<'[';rep(i,v.size())os< void fin(T a) { cout << a << '\n'; exit(0); } template bool chmin(T& a,T b) {if(a > b){a = b; return true;} return false;} template bool chmax(T& a,T b) {if(a < b){a = b; return true;} return false;} void scan(){} template void scan(Head& head, Tail&... tail){ cin >> head; scan(tail...); } template void print(const T& t){ cout << t << '\n'; } template void print(const Head& head, const Tail&... tail){ cout<= mod) x -= mod; return *this; } constexpr mint &operator++() { return *this += mint(1); } constexpr mint &operator-=(const mint &a) { if ((x += mod - a.x) >= mod) x -= mod; return *this; } constexpr mint &operator--() { return *this -= mint(1); } constexpr mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } constexpr mint operator+(const mint &a) const { mint res(*this); return res += a; } constexpr mint operator-(const mint &a) const { mint res(*this); return res -= a; } constexpr mint operator*(const mint &a) const { mint res(*this); return res *= a; } constexpr mint pow(ll t) const { mint res = mint(1), a(*this); while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } // for prime mod constexpr mint inv() const { return pow(mod - 2); } constexpr mint &operator/=(const mint &a) { return *this *= a.inv(); } constexpr mint operator/(const mint &a) const { mint res(*this); return res /= a; } }; ostream &operator<<(ostream &os, const mint &a) { return os << a.x; } bool operator==(const mint &a, const mint &b) { return a.x == b.x; } bool operator!=(const mint &a, const mint &b) { return a.x != b.x; } bool operator==(const mint &a, const int &b) { return a.x == b; } bool operator!=(const mint &a, const int &b) { return a.x != b; } class combination { vector fact, ifact; public: combination(int n) : fact(n + 1), ifact(n + 1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } } comb(400010); mint dp[10010][110]; mint tmp[110][110]; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); INT(n, m, l, K); chmin(K, l); vp pt; pt.eb(0, 0); rep(_, m) { INT(x, y); pt.eb(x, y); } pt.eb(n, n); m += 2; vvp tg(m); rep(_, l) { INT(x, y); auto it = lower_bound(all(pt), x, [](P val, int key) { return val.first < key; }); if (x < it->first) { auto bit = it; bit--; if (y > it->second or y < bit->second) continue; tg[it - pt.begin() - 1].eb(x - bit->first, y - bit->second); } else { assert(x == it->first); if (y == it->second) { K--; continue; } if (y < it->second) { auto bit = it; bit--; if (y < bit->second) continue; tg[it - pt.begin() - 1].eb(x - bit->first, y - bit->second); } else { auto nx = it; nx++; if (y > nx->second) continue; tg[it - pt.begin()].eb(0, y - it->second); } } } if (K < 0) fin(0); auto f = [](P a, P b) -> mint { auto[ax, ay] = a; auto[bx, by] = b; if (ax > bx or ay > by) return 0; int dx = bx - ax, dy = by - ay; return comb(dx + dy, dx); }; dp[0][0] = 1; rep(i, m - 1) { int x = pt[i + 1].first - pt[i].first; int y = pt[i + 1].second - pt[i].second; assert(x > 0 and y > 0); tg[i].eb(0, 0); tg[i].eb(x, y); sort(all(tg[i]), [](P a, P b) { return a.first + a.second < b.first + b.second; }); int sz = tg[i].size(); rep(j, sz) rep(k, sz) tmp[j][k] = 0; tmp[0][0] = 1; rep(j, sz) { vector to(sz); rep(k, j + 1, sz) { to[k] = f(tg[i][j], tg[i][k]); rep(p, j + 1, k) to[k] -= to[p] * f(tg[i][p], tg[i][k]); } rep(k, sz) { mint now = tmp[j][k]; if (now.x == 0) continue; rep(p, j + 1, sz) tmp[p][k + 1] += now * to[p]; } } rep(j, K + 1) { mint now = dp[i][j]; if (now.x == 0) continue; rep(k, sz - 1) { if (j + k > K) break; dp[i + 1][j + k] += now * tmp[sz - 1][k + 1]; } } } mint ans = 0; rep(i, K + 1) ans += dp[m - 1][i]; print(ans); }