#include #include #include #include #include #include #include #include #include using namespace std; template void chmax(T &x, T y) {if(x void chmin(T &x, T y) {if(x>y) x=y;} #ifndef Modint_hpp #define Modint_hpp #include #include template class modint { int val; public: constexpr modint() noexcept : val{0} {} constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {} constexpr long long value() const noexcept { return val; } constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; } constexpr modint &operator++() noexcept { return ++val, *this; } constexpr modint &operator--() noexcept { return --val, *this; } constexpr modint operator-() const noexcept { return modint(-val); } constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); } constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; } constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; } constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; } constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } constexpr bool operator!() const noexcept { return !val; } friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; } friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; } friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; } friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; } static constexpr modint inverse(const modint &other) noexcept { assert(other != 0); int a{mod}, b{other.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static constexpr modint pow(modint other, long long e) noexcept { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; } }; // class modint template <> class modint<2> { bool val; public: constexpr modint(bool x = false) noexcept : val{x} {} constexpr modint(int x) noexcept : val(x & 1) {} constexpr modint(long long x) noexcept : val(x & 1) {} constexpr operator bool() const noexcept { return val; } constexpr bool value() const noexcept { return val; } constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; } constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; } constexpr modint operator!() const noexcept { return !val; } constexpr modint operator-() const noexcept { return *this; } constexpr modint operator+(const modint &other) const noexcept { return val != other.val; } constexpr modint operator-(const modint &other) const noexcept { return val != other.val; } constexpr modint operator*(const modint &other) const noexcept { return val && other.val; } constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; } friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; } }; // class modint specialization #endif // Modint_hpp #include #include #include template class matrix { struct identity_wrapper { template struct check { static Ring identity() { return Ring::identity(); } }; template struct check { static Ring identity() { return 1; } }; operator Ring() { return check::value>::identity(); } }; using row_type = std::valarray; using data_type = std::valarray; data_type data; friend std::istream &operator>>(std::istream &is, matrix &mat) { for(size_t i = 0; i != mat.rows(); ++i) for(size_t j = 0; j != mat.columns(); ++j) is >> mat[i][j]; return is; } friend std::ostream &operator<<(std::ostream &os, const matrix &mat) { for(size_t i = 0; i != mat.rows(); ++i) { if(i) os << "\n"; for(size_t j = 0; j != mat.columns(); ++j) os << (j ? " " : "") << mat[i][j]; } return os; } friend matrix transpose(const matrix &mat) { matrix res(mat.columns(), mat.rows()); for(size_t i{mat.columns()}; i--;) for(size_t j{mat.rows()}; j--;) res[i][j] = mat[j][i]; return res; } public: explicit matrix(size_t _n = 1) : matrix(_n, _n) {} matrix(size_t _r, size_t _c) : data(row_type(_c), _r) {} matrix(const data_type &_data) : data(_data) {} size_t rows() const { return data.size(); } size_t columns() const { return data[0].size(); } row_type &operator[](const size_t i) { assert(i < data.size()); return data[i]; } const row_type &operator[](const size_t i) const { assert(i < data.size()); return data[i]; } matrix operator-() const { return {-data}; } matrix &operator+=(const matrix &rhs) { data += rhs.data; return *this; } matrix &operator-=(const matrix &rhs) { data -= rhs.data; return *this; } matrix &operator*=(matrix rhs) noexcept { assert(columns() == rhs.rows()); rhs = transpose(rhs); for(row_type &row : data) { const row_type copied{row}; for(size_t j{rhs.rows()}; j--;) row[j] = (copied * rhs[j]).sum(); } return *this; } matrix operator+(const matrix &rhs) const { return matrix{*this} += rhs; } matrix operator-(const matrix &rhs) const { return matrix{*this} -= rhs; } matrix operator*(const matrix &rhs) const { return matrix{*this} *= rhs; } friend row_type &operator*=(row_type &lhs, const matrix &rhs) { return lhs = lhs * rhs; } friend row_type operator*(row_type &lhs, const matrix &rhs) { assert(lhs.size() == rhs.rows()); row_type res(rhs.columns()); for(size_t k{lhs.size()}; k--;) for(size_t j{rhs.columns()}; j--;) res[j] += lhs[k] * rhs[k][j]; return res; } static matrix identity(const size_t _n) { matrix ide(_n); for(size_t i{_n}; i--;) ide[i][i] = identity_wrapper(); return ide; } friend matrix pow(matrix mat, unsigned long long exp) { matrix res{identity(mat.rows())}; for(assert(mat.rows() == mat.columns()); exp; mat *= mat, exp >>= 1) if(exp & 1) res *= mat; return res; } }; // class matrix main() { ios::sync_with_stdio(false), cin.tie(nullptr); using mint=modint<1000000007>; int n,w; long long k; cin>>n>>w>>k; vector a(n); for(auto &e:a) cin>>e; mint dp[200]; dp[0]=1; for(int i=0;i<100;++i) { for(int e:a) { dp[i+e]+=dp[i]; } } mint p=dp[w]; mint q=dp[w*2]-p*p; matrix res({{1,0},{0,1}}); matrix coef({{p,q},{1,0}}); while(k) { if(k&1) { res*=coef; } coef*=coef; k>>=1; } cout << res[1][0]*p+res[1][1] << "\n"; }