#include using namespace std; using lint = long long; const lint mod = 1e9 + 7; #define all(x) (x).begin(), (x).end() #define bitcount(n) __builtin_popcountl((lint)(n)) #define fcout cout << fixed << setprecision(15) #define highest(x) (63 - __builtin_clzl(x)) template inline void YES(T condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; } template inline void Yes(T condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; } templateint character_count(T text, U character){ int ans = 0; for(U i: text){ ans += (i == character); } return ans; } lint power(lint base, lint exponent, lint module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ lint root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }} struct position{ int y, x; }; position mv[4] = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; // double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); } template string to_string(pair x){ return to_string(x.first) + "," + to_string(x.second); } string to_string(string x){ return x; } template void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++) ans += to_string(*i) + " "; if(!ans.empty()) ans.pop_back(); cout << ans << endl; } template void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } } template T gcd(T a, T b){ if(a && b){ return gcd(min(a, b), max(a, b) % min(a, b)); }else{ return a; }} template T lcm(T a, T b){ return a / gcd(a, b) * b; } struct combination{ vector fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } lint C(int p, int q) const{ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } }; template bool next_sequence(itr first, itr last, int max_bound){ itr now = last; while(now != first){ now--; (*now)++; if((*now) == max_bound){ (*now) = 0; }else{ return true; } } return false; } template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; int N, W; lint K; vector A; lint dp[100]; lint jump(int remaining){ if(remaining == 0){ return 1; }else if(remaining < 0){ return 0; }else if(dp[remaining] != -1){ return dp[remaining]; } lint ans = 0; for(int i = 0; i < N; i++){ ans += jump(remaining - A[i]); } return dp[remaining] = ans % mod; } int main(){ cin >> N >> W >> K; A.resize(N); cins(all(A)); memset(dp, -1, sizeof(dp)); lint L1 = jump(W), L2 = (jump(W * 2) - L1 * L1 % mod + mod) % mod; auto A = Matrix(2, 2); A[0][0] = L1; A[0][1] = L2; A[1][0] = 1; A[1][1] = 0; auto x = Matrix(2, 1); x[0][0] = 1; x[1][0] = 0; A = A ^ K; x = A * x; cout << x[0][0] << endl; }