// #define DEBUGGING #include #define endl '\n' #define ALL(V) begin(V), end(V) #define ALLR(V) rbegin(V), rend(V) using ll = std::int64_t; using ull = std::uint64_t; using PLL = std::pair; using TLL = std::tuple; template using V = std::vector; template using VV = V>; template const T& var_min(const T &t) { return t; } template const T& var_max(const T &t) { return t; } template const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); } template const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); } template void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); } template void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); } template const T& clamp(const T &t, const T &low, const T &high) { return std::max(low, std::min(high, t)); } template void chclamp(T &t, const T &low, const T &high) { return t = clamp(t, low, high); } namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; } #define mv_rec make_v(init, tail...) template T make_v(T init) { return init; } template auto make_v(T init, size_t s, Tail... tail) { return V(s, mv_rec); } #undef mv_rec using namespace std; #ifdef DEBUGGING #else #define DEBUG(...) 0 #define DEBUG_SEPARATOR_LINE 0 #endif const ll mod = 1e9 + 7; ll mod_pow(ll n, ll k) { ll ret = 1; ll cur = n; while (k) { if (k & 1) ret = ret * cur % mod; cur = cur * cur % mod; k /= 2; } return ret; } const size_t SIZE = 40 * 2 + 10; ll dp[SIZE] = { 1 }; using Mat = VV; Mat mul(const Mat &m1, const Mat &m2) { Mat ret = make_v(0, m1.size(), m2[0].size()); for (ll i = 0; i < ret.size(); i++) for (ll j = 0; j < ret[0].size(); j++) { ll tmp = 0; for (ll k = 0; k < m2.size(); k++) tmp += m1[i][k] * m2[k][j] % mod; ret[i][j] = tmp % mod; } return ret; } Mat mod_pow(Mat m, ll k) { Mat ret = { { 1, 0, 0, }, { 0, 1, 0, }, { 0, 0, 1, }, }; Mat cur = m; while (k) { if (k & 1) ret = mul(ret, cur); cur = mul(cur, cur); k /= 2; } return ret; } ll solve() { ll N, W, K; cin >> N >> W >> K; V A(N); for (ll &e : A) cin >> e; for (ll i = 1; i < SIZE; i++) { for (ll e : A) { ll pre = i - e; if (pre < 0) continue; if (pre != 0 && pre % W == 0) continue; (dp[i] += dp[pre]) %= mod; } } if (K == 1) return dp[W]; Mat mat = { { dp[W], dp[2 * W], 0, }, { 1, 0, 0, }, { 0, 1, 0, }, }; Mat vec = { { dp[2], }, { dp[1], }, { dp[0], }, }; mat = mod_pow(mat, K + 1); auto ans = mul(mat, vec); return ans[1][0]; } int main() { cout << solve() << endl; return 0; }