using System; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Globalization; using System.IO; using System.Text; using System.Linq; using E = System.Linq.Enumerable; using System.Threading; using System.Numerics; internal partial class Solver { public void Run() { var n = ni(); var m = ni(); var a = nl(); var b = nl(); var mod = 998244353; ModInt.SetModValue(mod); var dp = new ModInt[m]; var B = new Binomial(m * 2 + 1, mod); for (int i = 0; i <= b; i++) { var to = (n - 1) * a; var rem = i - to; if (rem < 0) continue; dp[i] = B.H(n - 1, (int)rem); } for (int i = 0; i + 1 < dp.Length; i++) { dp[i + 1] += dp[i]; } ModInt ans = 0; for (int i = 0; i < m; i++) { var rem = m - i - 1; ans += dp[rem]; } for (int i = 0; i < n; i++) { ans *= i + 1; } cout.WriteLine(ans); } } public class Binomial { private readonly long[] factorial; private readonly long[] inverseFactorial; private readonly long[] inverse; private readonly int mod; public Binomial(int size, int primeMod) { size++; factorial = new long[size]; inverseFactorial = new long[size]; inverse = new long[size]; mod = primeMod; Setup(size); } private void Setup(int size) { factorial[0] = factorial[1] = 1; inverseFactorial[0] = inverseFactorial[1] = 1; inverse[1] = 1; for (int i = 2; i < size; i++) { factorial[i] = factorial[i - 1] * i % mod; inverse[i] = (mod - (mod / i) * inverse[mod % i] % mod); inverseFactorial[i] = inverseFactorial[i - 1] * inverse[i] % mod; } } public long C(int s, int t) { if (s < 0 || t < 0 || s < t) { return 0; } if (t == 0 || s == t) { return 1; } if (s >= mod) { return C(s % mod, t % mod) * C(s / mod, t / mod) % mod; // Lucas' theorem } return factorial[s] * inverseFactorial[t] % mod * inverseFactorial[s - t] % mod; } public long this[int s, int t] { get { return C(s, t); } } public long P(int s, int t) { if (s < 0 || t < 0 || s < t) return 0; return factorial[s] * inverseFactorial[s - t] % mod; } /// /// s 種類のものから重複を許して t 個選ぶ場合の数 /// /// public long H(int s, int t) { if (s < 0 || t < 0) return 0; if (s == 0 && t == 0) return 1; return C(s + t - 1, t); } public long H1(int s, int t) { return H(s, t - s); } } public struct ModInt : IEquatable { private static int mod = 0; private long _value; public ModInt(long x) { _value = x; Normalize(); } private static long RegularMod(long x, int mod) { if (x >= mod) { if (x < 2 * mod) { return x - mod; } return x % mod; } if (x >= 0) { return x; } x = mod - RegularMod(-x, mod); if (x == mod) { return 0; } return x; } public static int SetModValue(int m) { return mod = m; } private void Normalize() { _value = RegularMod(_value, mod); } public override string ToString() { return _value.ToString(CultureInfo.InvariantCulture); } public int ToInt() { return (int)_value; } public static bool operator ==(ModInt c1, ModInt c2) { return c1._value == c2._value; } public static bool operator !=(ModInt c1, ModInt c2) { return !(c1 == c2); } public static ModInt operator +(ModInt x, ModInt y) { return new ModInt(x._value + y._value); } public static ModInt operator -(ModInt x, ModInt y) { return new ModInt(x._value - y._value); } public static ModInt operator -(ModInt x) { return new ModInt(-x._value); } public static ModInt operator *(ModInt x, ModInt y) { return new ModInt(x._value * y._value); } public static ModInt operator /(ModInt x, ModInt y) { return new ModInt(x._value * Inverse(y._value, mod)); } public static ModInt operator ++(ModInt x) { return x + 1; } public static ModInt operator --(ModInt x) { return x - 1; } public static ModInt Pow(ModInt x, long n) { ModInt r = 1; while (n > 0) { if ((n & 1) != 0) { r *= x; } x *= x; n >>= 1; } return r; } private static long ExtendedGcd(long a, long b, ref long x, ref long y) { if (b == 0) { x = 1; y = 0; return a; } else { var d = ExtendedGcd(b, a % b, ref y, ref x); y -= a / b * x; return d; } } private static long Inverse(long a, long mod) { long x = 0, y = 0; if (ExtendedGcd(a, mod, ref x, ref y) == 1) { return (x + mod) % mod; } else { throw new Exception("Invalid inverse " + a + " " + mod); } } public static implicit operator ModInt(long x) { return new ModInt(x); } public override bool Equals(object obj) { if (obj == null) { return false; } return _value.Equals(((ModInt)obj)._value); } public override int GetHashCode() { return _value.GetHashCode(); } public bool Equals(ModInt other) { return _value.Equals(other._value); } } // PREWRITEN CODE BEGINS FROM HERE static public class StringExtensions { static public string JoinToString(this IEnumerable source, string separator = " ") { return string.Join(separator, source); } } internal partial class Solver : Scanner { static readonly int? StackSizeInMebiByte = null; //50; public static void StartAndJoin(Action action, int maxStackSize) { var thread = new Thread(new ThreadStart(action), maxStackSize); thread.Start(); thread.Join(); } public static void Main() { #if LOCAL byte[] inputBuffer = new byte[1000000]; var inputStream = Console.OpenStandardInput(inputBuffer.Length); using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) { Console.SetIn(reader); new Solver(Console.In, Console.Out).Run(); } #else Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); if (StackSizeInMebiByte.HasValue) { StartAndJoin(() => new Solver(Console.In, Console.Out).Run(), StackSizeInMebiByte.Value * 1024 * 1024); } else { new Solver(Console.In, Console.Out).Run(); } Console.Out.Flush(); #endif } #pragma warning disable IDE0052 private readonly TextReader cin; private readonly TextWriter cout; private readonly TextWriter cerr; #pragma warning restore IDE0052 public Solver(TextReader reader, TextWriter writer) : base(reader) { cin = reader; cout = writer; cerr = Console.Error; } public Solver(string input, TextWriter writer) : this(new StringReader(input), writer) { } #pragma warning disable IDE1006 #pragma warning disable IDE0051 private int ni() { return NextInt(); } private int[] ni(int n) { return NextIntArray(n); } private long nl() { return NextLong(); } private long[] nl(int n) { return NextLongArray(n); } private double nd() { return NextDouble(); } private double[] nd(int n) { return NextDoubleArray(n); } private string ns() { return Next(); } private string[] ns(int n) { return NextArray(n); } #pragma warning restore IDE1006 #pragma warning restore IDE0051 } #if DEBUG internal static class LinqPadExtension { public static string TextDump(this T obj) { if (obj is IEnumerable) return (obj as IEnumerable).Cast().JoinToString().Dump(); else return obj.ToString().Dump(); } public static T Dump(this T obj) { return LINQPad.Extensions.Dump(obj); } } #endif public class Scanner { private readonly TextReader Reader; private readonly CultureInfo ci = CultureInfo.InvariantCulture; private readonly char[] buffer = new char[2 * 1024]; private int cursor = 0, length = 0; private string Token; private readonly StringBuilder sb = new StringBuilder(1024); public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { Reader = reader; } public int NextInt() { return checked((int)NextLong()); } public long NextLong() { var s = Next(); long r = 0; int i = 0; bool negative = false; if (s[i] == '-') { negative = true; i++; } for (; i < s.Length; i++) { r = r * 10 + (s[i] - '0'); #if DEBUG if (!char.IsDigit(s[i])) throw new FormatException(); #endif } return negative ? -r : r; } public double NextDouble() { return double.Parse(Next(), ci); } public string[] NextArray(int size) { string[] array = new string[size]; for (int i = 0; i < size; i++) { array[i] = Next(); } return array; } public int[] NextIntArray(int size) { int[] array = new int[size]; for (int i = 0; i < size; i++) { array[i] = NextInt(); } return array; } public long[] NextLongArray(int size) { long[] array = new long[size]; for (int i = 0; i < size; i++) { array[i] = NextLong(); } return array; } public double[] NextDoubleArray(int size) { double[] array = new double[size]; for (int i = 0; i < size; i++) { array[i] = NextDouble(); } return array; } public string Next() { if (Token == null) { if (!StockToken()) { throw new Exception(); } } var token = Token; Token = null; return token; } public bool HasNext() { if (Token != null) { return true; } return StockToken(); } private bool StockToken() { while (true) { sb.Clear(); while (true) { if (cursor >= length) { cursor = 0; if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) { break; } } var c = buffer[cursor++]; if (33 <= c && c <= 126) { sb.Append(c); } else { if (sb.Length > 0) break; } } if (sb.Length > 0) { Token = sb.ToString(); return true; } return false; } } }