using System; using System.Collections; using System.Collections.Generic; using System.Globalization; using System.IO; using System.Linq; using E = System.Linq.Enumerable; internal partial class Solver { public void Run() { var mod = ModInt.SetModValue(1000000007); var n = ni(); var w = ni(); var k = nl(); var a = ni(n); var p = new ModInt[3 * w + 10]; p[0] = 1; for (int i = 1; i < p.Length; i++) { foreach (var x in a) { if (i - x >= 0) { p[i] += p[i - x]; } } } var M = new ModMatrix(2, 2); M[0, 0] = 0; M[0, 1] = 1; M[1, 0] = p[2 * w] - p[w] * p[w]; M[1, 1] = p[w]; var b = new ModMatrix(2, 1); b[0, 0] = 1; b[1, 0] = p[w]; var y = ModMatrix.Pow(M, k) * b; cout.WriteLine(y[0, 0]); } } public class ModMatrix { public int Row { get; private set; } public int Col { get; private set; } private ModInt[] Data; public ModMatrix(int row, int col) { Row = row; Col = col; Data = new ModInt[Row * Col]; } public ModMatrix(ModInt[,] array) : this(array.GetLength(0), array.GetLength(1)) { int index = 0; for (int i = 0; i < Row; i++) { for (int j = 0; j < Col; j++) { Data[index++] = array[i, j]; } } } public ModInt this[int row, int col] { set { Data[row * Col + col] = value; } get { return Data[row * Col + col]; } } public static ModMatrix UnitMatrix(int n) { var matrix = new ModMatrix(n, n); for (int i = 0; i < n; i++) { matrix[i, i] = 1; } return matrix; } public static ModMatrix operator +(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, A.Col); for (int i = 0; i < C.Data.Length; i++) { C.Data[i] = A.Data[i] + B.Data[i]; } return C; } public static ModMatrix operator -(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, A.Col); for (int i = 0; i < C.Data.Length; i++) { C.Data[i] = A.Data[i] - B.Data[i]; } return C; } public static ModMatrix operator *(ModMatrix A, ModMatrix B) { var C = new ModMatrix(A.Row, B.Col); for (int i = 0; i < A.Row; i++) { for (int j = 0; j < B.Col; j++) { var val = C[i, j]; for (int k = 0; k < A.Col; k++) { val += A[i, k] * B[k, j]; } C[i, j] = val; } } return C; } public static ModMatrix Pow(ModMatrix A, long n) { if (n == 0) { return UnitMatrix(A.Row); } if (n == 1) { return A; } ModMatrix result = A.Clone(), t = A.Clone(); n--; while (n > 0) { if ((n & 1) != 0) { result = result * t; } t = t * t; n >>= 1; } return result; } public ModMatrix Clone() { return new ModMatrix(Row, Col) { Data = Data.Clone() as ModInt[] }; } } public struct ModInt { 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, 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 { long 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(); } } // PREWRITEN CODE BEGINS FROM HERE internal partial class Solver : Scanner { public static void Main(string[] args) { #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 }); new Solver(Console.In, Console.Out).Run(); Console.Out.Flush(); #endif } #pragma warning disable IDE0052 private readonly TextReader cin; private readonly TextWriter cout; #pragma warning restore IDE0052 public Solver(TextReader reader, TextWriter writer) : base(reader) { cin = reader; cout = writer; } 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 } internal static class LinqPadExtension { public static T Dump(this T obj) { #if LOCAL return LINQPad.Extensions.Dump(obj); #else return obj; #endif } } public class Scanner { private readonly TextReader Reader; private readonly Queue TokenQueue = new Queue(); private readonly CultureInfo ci = CultureInfo.InvariantCulture; public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { Reader = reader; } public int NextInt() { return int.Parse(Next(), ci); } public long NextLong() { return long.Parse(Next(), ci); } 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 (TokenQueue.Count == 0) { if (!StockTokens()) { throw new InvalidOperationException(); } } return TokenQueue.Dequeue(); } public bool HasNext() { if (TokenQueue.Count > 0) { return true; } return StockTokens(); } private static readonly char[] _separator = new[] { ' ', '\t' }; private bool StockTokens() { while (true) { string line = Reader.ReadLine(); if (line == null) { return false; } string[] tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries); if (tokens.Length == 0) { continue; } foreach (string token in tokens) { TokenQueue.Enqueue(token); } return true; } } }