// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second #define INF32 (numeric_limits::max()/2-1) #define INF64 (numeric_limits::max()/2-1) #define INF (numeric_limits::max()/2-1) #ifdef LOCAL #include "debug.hpp" #define dump(...) cerr << "[" << setw(3) << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__) #define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl #define debug if (1) #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template using pque_max = priority_queue; template using pque_min = priority_queue, greater >; template ::value>::type> ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; } template ::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(v.begin(), v.end(), x)-v.begin(); } template int ubd(C const& v, T const& x) { return upper_bound(v.begin(), v.end(), x)-v.begin(); } // <<< // >>> modint template class modint { static_assert(md > 0, ""); using M = modint; using ll = int64_t; int32_t x; public: static constexpr int32_t mod = md; constexpr modint(ll x = 0) : x((x%=mod) < 0 ? x+mod : x) { } constexpr ll val() const { return x; } constexpr explicit operator ll() const { return x; } constexpr bool operator==(M const& r) const { return x == r.x; } constexpr bool operator!=(M const& r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M const& r) { ll t = ll(x) + r.x; if (t >= mod) t -= mod; x = t; return *this; } constexpr M& operator-=(M const& r) { ll t = ll(x) + mod-r.x; if (t >= mod) t -= mod; x = t; return *this; } constexpr M& operator*=(M const& r) { return *this = *this * r; } constexpr M operator*(M const& r) const { M t; t.x = (ll(x)*r.x) % mod; return t; } constexpr M& operator/=(M const& r) { return *this *= r.inv(); } constexpr M operator+(M const& r) const { return M(*this) += r; } constexpr M operator-(M const& r) const { return M(*this) -= r; } constexpr M operator/(M const& r) const { return M(*this) /= r; } friend constexpr M operator+(ll x, M const& y) { return M(x)+y; } friend constexpr M operator-(ll x, M const& y) { return M(x)-y; } friend constexpr M operator*(ll x, M const& y) { return M(x)*y; } friend constexpr M operator/(ll x, M const& y) { return M(x)/y; } constexpr M pow(ll n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } constexpr M inv() const { assert(x > 0); ll t = 1, v = x, q = 0, r = 0; while (v != 1) { q = mod / v; r = mod % v; if (r * 2 < v) { t *= -q; t %= mod; v = r; } else { t *= q + 1; t %= mod; v -= r; } } if (t < 0) t += mod; M y; y.x = t; return y; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { int64_t x; is >> x; r = x; return is; } }; // <<< //constexpr int64_t MOD = 998244353; constexpr int64_t MOD = 1e9+7; using mint = modint<(int32_t)MOD>; // >>> matrix template struct Matrix { int n,m; vector > a; Matrix() {} Matrix(int n, int m) : n(n), m(m), a(n) { assert(n > 0 && m > 0); rep (i,n) a[i].resize(m); } Matrix(initializer_list > init) { for (auto ls : init) { a.emplace_back(); for (auto x : ls) a.back().emplace_back(x); } n = a.size(); assert(n > 0); m = a[0].size(); assert(m > 0); } vector const& operator[](int i) const { assert(0 <= i && i < n); return a[i]; } vector & operator[](int i) { assert(0 <= i && i < n); return a[i]; } bool operator==(Matrix const& x) const { if (n != x.n || m != x.m) return false; rep (i,n) rep (j,m) if (a[i][j] != x[i][j]) return false; return true; } bool operator!=(Matrix const& x) const { return !(*this == x); } Matrix& operator+=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] += x[i][j]; return *this; } Matrix& operator-=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] -= x[i][j]; return *this; } Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; } Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; } Matrix operator*(Matrix const& x) const { assert(m == x.n); Matrix ret(n,x.m); rep (i,n) rep (j,m) rep (k,x.m) ret[i][k] += a[i][j] * x[j][k]; return ret; } Matrix& operator*=(Matrix const& x) { auto res = (*this)*x; swap(a, res.a); return *this; } Matrix operator+() const { return *this; } Matrix operator-() const { Matrix x = *this; rep (i,n) rep (j,m) x[i][j] = -x[i][j]; return x; } Matrix& operator*=(T const& c) { rep (i,n) rep (j,m) a[i][j] *= c; return *this; } Matrix operator*(T const& c) const { return Matrix(*this) *= c; } friend Matrix operator*(T const& c, Matrix const& x) { Matrix ret = x; rep (i,x.n) rep (j,x.m) ret[i][j] = c*x[i][j]; return ret; } Matrix& operator/=(T const& c) { rep (i,n) rep (j,m) a[i][j] /= c; return *this; } Matrix operator/(T const& c) const { return Matrix(*this) /= c; } static Matrix identity(int n) { Matrix ret(n,n); rep (i,n) ret[i][i] = 1; return ret; } Matrix pow(ll k) const { assert(n == m); assert(k >= 0); Matrix v = *this, r = Matrix::identity(n); for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v; return r; } friend istream& operator>>(istream& is, Matrix& x) { rep (i,x.n) rep (j,x.m) is >> x[i][j]; return is; } #ifdef LOCAL friend string to_s(Matrix const& x) { string ret; rep (i,x.n) { ret += "\n("; rep (j,x.m) ret += " " + to_s(x[i][j]); ret += " )"; } return ret += "\n"; } #endif }; // <<< int32_t main() { int n,w,k; cin >> n >> w >> k; vector a(n); cin >> a; vector dp(2*w+1); dp[0] = 1; rep (i,sz(dp)) rep (j,n) { if (i+a[j] < sz(dp)) dp[i+a[j]] += dp[i]; } Matrix mat = { { dp[w], dp[2*w]-dp[w]*dp[w] }, { 1, 0 } }; auto res = mat.pow(k-1); cout << res[0][0]*dp[w] + res[0][1]*1 << endl; }