#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> template void debug(T e) { cerr << e << endl; } template void debug(vector &v) { rep(i, v.size()) { cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v) { rep(i, v.size()) { rep(j, v[i].size()) { cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v) { rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st) { for (auto itr = st.begin(); itr != st.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms) { for (auto itr = ms.begin(); itr != ms.end(); itr++) { cerr << *itr << " "; } cerr << endl; } template void debug(map &mp) { for (auto itr = mp.begin(); itr != mp.end(); itr++) { cerr << itr->first << " " << itr->second << endl; } } void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << H << " "; debug_out(T...); } using mint = modint998244353; void debug_mint1(vector &vec) { for (int i = 0; i < vec.size(); i++) { cerr << vec[i].val() << " "; } cerr << endl; } void debug_mint2(vector> &vec) { for (int i = 0; i < vec.size(); i++) { for (int j = 0; j < vec[i].size(); j++) { cerr << vec[i][j].val() << " "; } cerr << endl; } } mint comb(ll n, ll r, vector &fact, vector &finv) { if (n < r) { return mint(0); } else if (r < 0) { return mint(0); } return fact[n] * finv[n - r] * finv[r]; } mint routes(ll dx, ll dy, vector &fact, vector &finv) { return comb(dx + dy, dx, fact, finv); } int main() { ll N, M, L, K; cin >> N >> M >> L >> K; vector xc(M + 2); vector yc(M + 2); for (ll i = 0; i < M; i++) { cin >> xc[i + 1] >> yc[i + 1]; } xc[0] = 0; yc[0] = 0; xc[M + 1] = N; yc[M + 1] = N; vector xt(L); vector yt(L); for (ll i = 0; i < L; i++) { cin >> xt[i] >> yt[i]; } vector fact(2 * N + 1); vector finv(2 * N + 1); fact[0] = 1; finv[0] = 1; for (ll i = 0; i < 2 * N; i++) { fact[i + 1] = fact[i] * mint(i + 1); finv[i + 1] = 1 / fact[i + 1]; } vector> p(M + 1, vector(0)); for (ll i = 0; i < M + 1; i++) { p[i].push_back(make_pair(xc[i], yc[i])); p[i].push_back(make_pair(xc[i + 1], yc[i + 1])); } vector tigar(M + 1, false); for (ll i = 0; i < M + 1; i++) { for (ll j = 0; j < L; j++) { if (xc[i] <= xt[j] && xt[j] <= xc[i + 1] && yc[i] <= yt[j] && yt[j] <= yc[i + 1] && !(xc[i] == xt[j] && yc[i] == yt[j]) && !(xc[i + 1] == xt[j] && yc[i + 1] == yt[j])) { p[i].push_back(make_pair(xt[j], yt[j])); } if (xc[i + 1] == xt[j] && yc[i + 1] == yt[j]) { tigar[i] = true; } } } for (ll i = 0; i < M + 1; i++) { sort(all(p[i])); } // 素直に dp をすればよいはず vector> dp(M + 2, vector(L + 1, 0)); dp[0][0] = 1; for (ll i = 0; i < M + 1; i++) { ll len = p[i].size(); vector> subdp(len, vector(len + 2, 0)); subdp[0][0] = 1; for (ll j = 1; j < len; j++) { for (ll m = len; m >= 0; m--) { for (ll k = 0; k < j; k++) { ll fx = p[i][k].first; ll fy = p[i][k].second; ll tx = p[i][j].first; ll ty = p[i][j].second; // debug_out(fx, fy, tx, ty, // routes(tx - fx, ty - fy, fact, finv).val()); if (j == len - 1) { subdp[j][m] += subdp[k][m] * routes(tx - fx, ty - fy, fact, finv); } else { subdp[j][m + 1] += subdp[k][m] * routes(tx - fx, ty - fy, fact, finv); } } if (!(m == 0 && j < len - 1)) { for (ll k = m + 1; k <= len + 1; k++) { subdp[j][m] -= subdp[j][k]; } } } } for (ll j = 0; j <= L; j++) { for (ll k = 0; k <= len; k++) { if (j + k + tigar[i] <= L) { dp[i + 1][j + k + tigar[i]] += dp[i][j] * subdp[len - 1][k]; } } } // debug_mint2(subdp); } // 答えを求めたい mint ans = 0; for (ll i = 0; i <= L; i++) { if (i <= K) { ans += dp[M + 1][i]; } } cout << ans.val() << endl; }