using System; using System.IO; using System.Collections.Generic; using System.Linq; using System.Numerics; using System.Runtime.CompilerServices; using System.Text; using System.Globalization; using System.Threading; using static System.Math; namespace FertiLib.Contest.E { public class Solver { Scanner sr; StreamWriter sw; bool isMultipleTestCases = false; ModInt[] factorial, finv; public void Solve() { Init(); var (n, m, l, k) = sr.ReadValue(); var checkpoint = new List<(int x, int y)>(); var checkx = new List(); checkpoint.Add((0, 0)); checkx.Add(0); for (int i = 0; i < m; i++) { var xy = sr.ReadValue(); checkpoint.Add(xy); checkx.Add(xy.Item1); } checkpoint.Add((n, n)); checkx.Add(n); var square = new List<(int x, int y)>(); for (int i = 0; i < checkpoint.Count - 1; i++) { square.Add((checkpoint[i + 1].x - checkpoint[i].x, checkpoint[i + 1].y - checkpoint[i].y)); } var tiger = Enumerable.Repeat(0, m + 1).Select(p => new List<(int x, int y)>()).ToArray(); for (int i = 0; i < l; i++) { var (x, y) = sr.ReadValue(); var ok = -1; var ng = m + 1; while (ng - ok > 1) { var mid = ok + (ng - ok) / 2; if (x >= checkpoint[mid].x && y >= checkpoint[mid].y) ok = mid; else ng = mid; } var index = ok; if (x < checkpoint[index].x || x > checkpoint[index + 1].x) continue; if (y < checkpoint[index].y || y > checkpoint[index + 1].y) continue; tiger[index].Add((x - checkpoint[index].x, y - checkpoint[index].y)); } for (int i = 0; i < m + 1; i++) { tiger[i].Sort(); } var ans = new ModInt[l + 1]; ans[0] = 1; for (int i = 0; i < m + 1; i++) { if (tiger[i].Count == 0) { var all = Binom(square[i].x + square[i].y, square[i].x); for (int j = 0; j < l + 1; j++) { ans[j] *= all; } continue; } ModInt t = 0; var exclude = Enumerable.Repeat(0, tiger[i].Count).Select(p => new ModInt[tiger[i].Count + 1]).ToArray(); for (int j = 0; j < tiger[i].Count; j++) { var all = Binom(tiger[i][j].x + tiger[i][j].y, tiger[i][j].x); ModInt sum = 0; for (int p = tiger[i].Count; p >= 1; p--) { if (p == 1) exclude[j][p] += all; for (int s = 0; s < j; s++) { var x = tiger[i][j].x - tiger[i][s].x; var y = tiger[i][j].y - tiger[i][s].y; if (x < 0 || y < 0) continue; exclude[j][p] += exclude[s][p - 1] * Binom(x + y, x); } exclude[j][p] -= sum; sum += exclude[j][p]; } } { var all = Binom(square[i].x + square[i].y, square[i].x); var way = new ModInt[tiger[i].Count + 1]; ModInt sum = 0; for (int p = tiger[i].Count; p >= 0; p--) { if (p == 0) way[p] += all; for (int s = 0; s < tiger[i].Count; s++) { var x = square[i].x - tiger[i][s].x; var y = square[i].y - tiger[i][s].y; way[p] += exclude[s][p] * Binom(x + y, x); } way[p] -= sum; sum += way[p]; } var next = new ModInt[l + 1]; for (int s = l; s >= 0; s--) { for (int u = tiger[i].Count; u >= 0; u--) { if (s + u > l) continue; next[s + u] += ans[s] * way[u]; } } ans = next; } } ModInt ansall = 0; for (int i = 0; i <= Min(k, l); i++) { ansall += ans[i]; } Console.WriteLine(ansall); } public ModInt Binom(int n, int r) => factorial[n] * finv[r] * finv[n - r]; public void Init() { factorial = new ModInt[400005]; finv = new ModInt[400005]; factorial[0] = 1; finv[0] = 1; for (int i = 1; i < 400005; i++) { factorial[i] = factorial[i - 1] * i; finv[i] = factorial[i].Inverse(); } } public Solver(Scanner cin, StreamWriter cout) { this.sr = cin; this.sw = cout; } public void Start() { int _t = 1; if (isMultipleTestCases) _t = sr.ReadInt(); while (_t-- > 0) Solve(); } public static void YESNO(bool condition) => Console.WriteLine(condition ? "YES" : "NO"); public static void YesNo(bool condition) => Console.WriteLine(condition ? "Yes" : "No"); public static void yesno(bool condition) => Console.WriteLine(condition ? "yes" : "no"); } public struct ModInt : IEquatable { public static long MOD = 998244353; public static bool isModPrime { get; set; } private readonly long num; public ModInt(long n) { num = n; isModPrime = true; } public override string ToString() => num.ToString(); public static ModInt operator +(ModInt l, ModInt r) { long x = l.num + r.num; if (x >= MOD) x -= MOD; return new ModInt(x); } public static ModInt operator -(ModInt l, ModInt r) { long x = l.num - r.num; if (x < 0) x += MOD; return new ModInt(x); } public static ModInt operator *(ModInt l, ModInt r) => new ModInt((l.num * r.num) % MOD); public static ModInt operator /(ModInt l, ModInt r) => l * r.Inverse(); public static ModInt operator ++(ModInt x) { var tmp = x + new ModInt(1); return tmp; } public static ModInt operator --(ModInt x) { var tmp = x - new ModInt(1); return tmp; } public static bool operator ==(ModInt l, ModInt r) => l.Equals(r); public static bool operator !=(ModInt l, ModInt r) => !l.Equals(r); public static implicit operator long(ModInt x) => x.num; public static implicit operator ModInt(long n) { n %= MOD; if (n < 0) n += MOD; return new ModInt(n); } public ModInt Inverse() => Inverse(this, MOD); public static ModInt Inverse(ModInt x) => Inverse(x.num, MOD); public static long Inverse(long x, long m) { if (x % m == 0) throw new DivideByZeroException(); long a = x, b = m, u = 1, v = 0; while (b > 0) { long t = a / b; a -= t * b; long p = a; a = b; b = p; // swap(a, b); u -= t * v; p = u; u = v; v = p; // swap(u, v); } u %= m; if (u < 0) u += m; return u; } public ModInt Pow(long n) => Pow(this, n); public static ModInt Pow(long x, long n) { if (n < 0) return Pow(x, -n).Inverse(); x %= MOD; long now = 1; if (isModPrime) n %= MOD - 1; for (; n > 0; n /= 2, x = x * x % MOD) { if (n % 2 == 1) now = now * x % MOD; } return new ModInt(now); } public bool Equals(ModInt x) => num == x.num; public override bool Equals(object obj) => obj is ModInt m && num == m.num; public override int GetHashCode() { return HashCode.Combine(num); } } public static class Program { public static void Main(string[] args) { var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw); var cin = new Scanner(); var solver = new Solver(cin, sw); solver.Start(); Console.Out.Flush(); } } public static class Extention { public static string Join(this IEnumerable x, string separator = "") => string.Join(separator, x); public static int UpperBound(this IList list, T value) => list.BinarySearch(value, true, 0, list.Count, Comparer.Default); public static int LowerBound(this IList list, T value) => list.BinarySearch(value, false, 0, list.Count, Comparer.Default); public static int BinarySearch(this IList list, T value, bool isUpperBound, int index, int length, Comparer comparer) { var ng = index - 1; var ok = index + length; while (ok - ng > 1) { var mid = ng + (ok - ng) / 2; var res = comparer.Compare(list[mid], value); if (res < 0 || (isUpperBound && res == 0)) ng = mid; else ok = mid; } return ok; } public static bool Chmax(ref this T a, T b) where T : struct, IComparable { if (a.CompareTo(b) >= 0) return false; a = b; return true; } public static bool Chmin(ref this T a, T b) where T : struct, IComparable { if (a.CompareTo(b) <= 0) return false; a = b; return true; } } public class Scanner { string[] s; int i; char[] separator = new char[] { ' ' }; public Scanner() { s = new string[0]; i = 0; } public string Read() => ReadString(); public string ReadString() { if (i < s.Length) return s[i++]; string st = Console.ReadLine(); while (st == "") st = Console.ReadLine(); s = st.Split(separator, StringSplitOptions.RemoveEmptyEntries); if (s.Length == 0) return ReadString(); i = 0; return s[i++]; } public string[] ReadStringArray(int N) { string[] Array = new string[N]; for (int i = 0; i < N; i++) { Array[i] = ReadString(); } return Array; } public int ReadInt() => int.Parse(ReadString()); public int[] ReadIntArray(int N, int add = 0) { int[] Array = new int[N]; for (int i = 0; i < N; i++) { Array[i] = ReadInt() + add; } return Array; } public long ReadLong() => long.Parse(ReadString()); public long[] ReadLongArray(int N, long add = 0) { long[] Array = new long[N]; for (int i = 0; i < N; i++) { Array[i] = ReadLong() + add; } return Array; } public double ReadDouble() => double.Parse(ReadString()); public double[] ReadDoubleArray(int N, double add = 0) { double[] Array = new double[N]; for (int i = 0; i < N; i++) { Array[i] = ReadDouble() + add; } return Array; } public T1 ReadValue() => (T1)Convert.ChangeType(ReadString(), typeof(T1)); public (T1, T2) ReadValue() { var inputs = ReadStringArray(2); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); return (v1, v2); } public (T1, T2, T3) ReadValue() { var inputs = ReadStringArray(3); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); return (v1, v2, v3); } public (T1, T2, T3, T4) ReadValue() { var inputs = ReadStringArray(4); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); return (v1, v2, v3, v4); } public (T1, T2, T3, T4, T5) ReadValue() { var inputs = ReadStringArray(5); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); return (v1, v2, v3, v4, v5); } public (T1, T2, T3, T4, T5, T6) ReadValue() { var inputs = ReadStringArray(6); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6)); return (v1, v2, v3, v4, v5, v6); } public (T1, T2, T3, T4, T5, T6, T7) ReadValue() { var inputs = ReadStringArray(7); var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1)); var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2)); var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3)); var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4)); var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5)); var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6)); var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7)); return (v1, v2, v3, v4, v5, v6, v7); } public T1[] ReadValueArray(int N) { var v1 = new T1[N]; for (int i = 0; i < N; i++) { v1[i] = ReadValue(); } return v1; } public (T1[], T2[]) ReadValueArray(int N) { var (v1, v2) = (new T1[N], new T2[N]); for (int i = 0; i < N; i++) { var (t1, t2) = ReadValue(); v1[i] = t1; v2[i] = t2; } return (v1, v2); } public (T1[], T2[], T3[]) ReadValueArray(int N) { var (v1, v2, v3) = (new T1[N], new T2[N], new T3[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3) = ReadValue(); v1[i] = t1; v2[i] = t2; v3[i] = t3; } return (v1, v2, v3); } public (T1[], T2[], T3[], T4[]) ReadValueArray(int N) { var (v1, v2, v3, v4) = (new T1[N], new T2[N], new T3[N], new T4[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4) = ReadValue(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; } return (v1, v2, v3, v4); } public (T1[], T2[], T3[], T4[], T5[]) ReadValueArray(int N) { var (v1, v2, v3, v4, v5) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5) = ReadValue(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; } return (v1, v2, v3, v4, v5); } public (T1[], T2[], T3[], T4[], T5[], T6[]) ReadValueArray(int N) { var (v1, v2, v3, v4, v5, v6) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5, t6) = ReadValue(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; v6[i] = t6; } return (v1, v2, v3, v4, v5, v6); } public (T1[], T2[], T3[], T4[], T5[], T6[], T7[]) ReadValueArray(int N) { var (v1, v2, v3, v4, v5, v6, v7) = (new T1[N], new T2[N], new T3[N], new T4[N], new T5[N], new T6[N], new T7[N]); for (int i = 0; i < N; i++) { var (t1, t2, t3, t4, t5, t6, t7) = ReadValue(); v1[i] = t1; v2[i] = t2; v3[i] = t3; v4[i] = t4; v5[i] = t5; v6[i] = t6; v7[i] = t7; } return (v1, v2, v3, v4, v5, v6, v7); } } }