#ifndef CLASS_MODINT #define CLASS_MODINT #include template class modint { private: std::uint32_t n; public: modint() : n(0) {}; modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {}; static constexpr std::uint32_t get_mod() { return mod; } std::uint32_t get() const { return n; } bool operator==(const modint& m) const { return n == m.n; } bool operator!=(const modint& m) const { return n != m.n; } modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; } modint operator+(const modint& m) const { return modint(*this) += m; } modint operator-(const modint& m) const { return modint(*this) -= m; } modint operator*(const modint& m) const { return modint(*this) *= m; } modint inv() const { return (*this).pow(mod - 2); } modint pow(std::uint64_t b) const { modint ans = 1, m = modint(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } }; #endif // CLASS_MODINT #include #include #include using namespace std; using mint = modint<1000000007>; vector > matrix_mul(int N, vector > A, vector > B) { vector > C(N, vector(N, mint(0))); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { for (int k = 0; k < N; k++) { C[i][j] += A[i][k] * B[k][j]; } } } return C; } int main() { long long L; int N, M; cin >> L >> N >> M; vector K(M); for (int i = 0; i < M; i++) { cin >> K[i]; } vector > g; for (int i = 0; i <= N; i++) { for (int j = 1; j <= i + 1; j++) { g.push_back(make_pair(i, j)); } } int D = g.size(); vector > base_matrix(D, vector(D)); for (int i = 0; i < D; i++) { for (int j = 0; j < D; j++) { if (i == 0) { base_matrix[i][j] = (j != 0 && g[j].second == 1 ? 1 : 0); } else { base_matrix[i][j] = (g[j].first == g[i].first ? (g[j].second == min(g[i].second + 1, g[i].first + 1) ? 1 : 0) : ((g[i].first != g[i].second || find(K.begin(), K.end(), g[i].first) == K.end()) && j != 0 && g[j].second == 1 ? 1 : 0)); } } } vector > M1(D, vector(D, mint(0))), M2 = base_matrix; for (int i = 0; i < D; i++) { M1[i][i] = 1; } long long CL = L; while (CL > 0) { if (CL % 2 == 1) { M1 = matrix_mul(D, M1, M2); } M2 = matrix_mul(D, M2, M2); CL /= 2; } mint answer = 0; for (int i = 0; i < D; i++) { if (i != 0 && (g[i].first != g[i].second || find(K.begin(), K.end(), g[i].first) == K.end())) { answer += M1[0][i]; } } mint remains = mint(N).pow(L); cout << (remains - answer).get() << endl; return 0; }