using System; using CompLib.Mathematics; using CompLib.Util; class Program { private int N, W; private long K; private int[] A; public void Solve() { var sc = new Scanner(); N = sc.NextInt(); W = sc.NextInt(); K = sc.NextLong(); A = sc.IntArray(); // 0 -> Wに行くパターン数 // 0 -> Wを飛ばして2Wに行く var dp = new ModInt[2 * W + 1]; dp[0] = 1; for (int i = 0; i < 2 * W; i++) { if (i == W) continue; foreach (int j in A) { if (i + j <= 2 * W) dp[i + j] += dp[i]; } } // 0 -> W dp[W] // 0 -> 2W W飛ばす dp[2W] var p = new Matrix(1, 2); p[0, 0] = 1; p[0, 1] = dp[W]; var m = new Matrix(2, 2); m[0, 0] = 0; m[0, 1] = dp[2 * W]; m[1, 0] = 1; m[1, 1] = dp[W]; var t = Matrix.Pow(m, K); var ans = p * t; Console.WriteLine(ans[0, 0]); } public static void Main(string[] args) => new Program().Solve(); } // https://bitbucket.org/camypaper/complib namespace CompLib.Mathematics { using System.Diagnostics; using N = ModInt; #region Matrix public class Matrix { int row, col; public N[] mat; /// /// 列目の要素へのアクセスを提供します。 /// /// 行の番号 /// 列の番号 public N this[int r, int c] { get { return mat[r * col + c]; } set { mat[r * col + c] = value; } } public Matrix(int r, int c) { row = r; col = c; mat = new N[row * col]; } public static Matrix operator *(Matrix l, Matrix r) { Debug.Assert(l.col == r.row); var ret = new Matrix(l.row, r.col); for (int i = 0; i < l.row; i++) for (int k = 0; k < l.col; k++) for (int j = 0; j < r.col; j++) ret.mat[i * r.col + j] = (ret.mat[i * r.col + j] + l.mat[i * l.col + k] * r.mat[k * r.col + j]); return ret; } /// /// ^ を O(^3 log ) で計算します。 /// public static Matrix Pow(Matrix m, long n) { var ret = new Matrix(m.row, m.col); for (int i = 0; i < m.row; i++) ret.mat[i * m.col + i] = 1; for (; n > 0; m *= m, n >>= 1) if ((n & 1) == 1) ret = ret * m; return ret; } public N[][] Items { get { var a = new N[row][]; for (int i = 0; i < row; i++) { a[i] = new N[col]; for (int j = 0; j < col; j++) a[i][j] = mat[i * col + j]; } return a; } } } #endregion } // https://bitbucket.org/camypaper/complib namespace CompLib.Mathematics { #region ModInt /// /// [0,) までの値を取るような数 /// public struct ModInt { /// /// 剰余を取る値. /// public const long Mod = (int) 1e9 + 7; /// /// 実際の数値. /// public long num; /// /// 値が であるようなインスタンスを構築します. /// /// インスタンスが持つ値 /// パフォーマンスの問題上,コンストラクタ内では剰余を取りません.そのため, ∈ [0,) を満たすような を渡してください.このコンストラクタは O(1) で実行されます. public ModInt(long n) { num = n; } /// /// このインスタンスの数値を文字列に変換します. /// /// [0,) の範囲内の整数を 10 進表記したもの. public override string ToString() { return num.ToString(); } public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; } public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; } public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); } public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); } /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); } /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(long v, long k) { long ret = 1; for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod) if ((k & 1) == 1) ret = ret * v % Mod; return new ModInt(ret); } /// /// 与えられた数の逆元を計算します. /// /// 逆元を取る対象となる数 /// 逆元となるような値 /// 法が素数であることを仮定して,フェルマーの小定理に従って逆元を O(log N) で計算します. public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); } } #endregion #region Binomial Coefficient public class BinomialCoefficient { public ModInt[] fact, ifact; public BinomialCoefficient(int n) { fact = new ModInt[n + 1]; ifact = new ModInt[n + 1]; fact[0] = 1; for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i; ifact[n] = ModInt.Inverse(fact[n]); for (int i = n - 1; i >= 0; i--) ifact[i] = ifact[i + 1] * (i + 1); ifact[0] = ifact[1]; } public ModInt this[int n, int r] { get { if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0; return fact[n] * ifact[n - r] * ifact[r]; } } public ModInt RepeatedCombination(int n, int k) { if (k == 0) return 1; return this[n + k - 1, k]; } } #endregion } namespace CompLib.Util { using System; using System.Linq; class Scanner { private string[] _line; private int _index; private const char Separator = ' '; public Scanner() { _line = new string[0]; _index = 0; } public string Next() { while (_index >= _line.Length) { _line = Console.ReadLine().Split(Separator); _index = 0; } return _line[_index++]; } public int NextInt() => int.Parse(Next()); public long NextLong() => long.Parse(Next()); public double NextDouble() => double.Parse(Next()); public decimal NextDecimal() => decimal.Parse(Next()); public char NextChar() => Next()[0]; public char[] NextCharArray() => Next().ToCharArray(); public string[] Array() { _line = Console.ReadLine().Split(' '); _index = _line.Length; return _line; } public int[] IntArray() => Array().Select(int.Parse).ToArray(); public long[] LongArray() => Array().Select(long.Parse).ToArray(); public double[] DoubleArray() => Array().Select(double.Parse).ToArray(); public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray(); } }