#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #define all(x) (x).begin(),(x).end() //#pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60; templatebool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } templatebool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } #ifndef TEST #define assert(x) #endif //--------------------------------------------------------------------------------------------------- template struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) { } ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } return ModInt(u); } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template ostream& operator<<(ostream& st, const ModInt a) { st << a.get(); return st; }; template ModInt operator^(ModInt a, unsigned long long k) { ModInt r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<1000000007> mint; int mod = 1000000007; int add(int x, int y) { return (x += y) >= mod ? x - mod : x; } template int add(int x, T... y) { return add(x, add(y...)); } int mul(int x, int y) { return 1LL * x * y % mod; } template int mul(int x, T... y) { return mul(x, mul(y...)); } int sub(int x, int y) { return add(x, mod - y); } int modpow(int a, long long b) { int ret = 1; while (b > 0) { if (b & 1) ret = 1LL * ret * a % mod; a = 1LL * a * a % mod; b >>= 1; } return ret; } int modinv(int a) { return modpow(a, mod - 2); } typedef vector Vec; typedef vector Mat; Vec mulMatVec(Mat a, Vec b) { int n = b.size(); Vec ret(n, 0); rep(i, 0, n) rep(j, 0, n) ret[i] = add(ret[i], mul(a[i][j], b[j])); return ret; } Mat mulMatMat(Mat a, Mat b) { int n = a.size(); Mat ret(n, Vec(n, 0)); rep(i, 0, n) rep(j, 0, n) rep(k, 0, n) ret[i][j] = add(ret[i][j], mul(a[i][k], b[k][j])); return ret; } Mat fastpow(Mat x, ll n) { Mat ret(x.size(), Vec(x.size(), 0)); rep(i, 0, x.size()) ret[i][i] = 1; while (0 < n) { if ((n % 2) == 0) { x = mulMatMat(x, x); n >>= 1; } else { ret = mulMatMat(ret, x); --n; } } return ret; } void printVec(Vec a) { cout << "[\t"; rep(i, 0, a.size()) cout << a[i] << "\t"; cout << "]" << endl; } void printMat(Mat a) { rep(i, 0, a.size()) printVec(a[i]); } // example: n=2 // x[0] = init[0], x[1] = init[1] // x[i] = co[0] * x[i-1] + co[1] * x[i-2] int solveLinearRecurrenceFormula(vector init, vector coefficient, ll idx) { assert(init.size() == coefficient.size()); int n = init.size(); Vec v = init; Mat m(n, Vec(n, 0)); rep(i, 0, n - 1) m[i][i + 1] = 1; rep(i, 0, n) m[n - 1][i] = coefficient[n - 1 - i]; m = fastpow(m, idx); v = mulMatVec(m, v); return v[0]; } /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i @hamayanhamayan0     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ int N, W, A[101]; ll K; mint dp[201]; //--------------------------------------------------------------------------------------------------- void _main() { cin >> N >> W >> K; rep(i, 0, N) cin >> A[i]; dp[0] = 1; rep(cu, 0, W * 2) rep(i, 0, N) dp[cu + A[i]] += dp[cu]; dp[2 * W] -= dp[W] * dp[W]; int ans = solveLinearRecurrenceFormula({ dp[0].get(), dp[W].get() }, { dp[W].get(), dp[2 * W].get() }, K); cout << ans << endl; }