#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 == v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const array& v) { for (size_t i = 0; i < N; i++) { os << v[i] << (i + 1 == N ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) void(0) #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } long long MSK(int n) { return (1LL << n) - 1; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } template void mkuni(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } template int lwb(const vector& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); } #pragma endregion #include #include "atcoder/modint" namespace atcoder { template std::istream& operator>>(std::istream& is, static_modint& x) { int64_t v; x = static_modint{(is >> v, v)}; return is; } template std::ostream& operator<<(std::ostream& os, const static_modint& x) { return os << x.val(); } template std::ostream& operator<<(std::ostream& os, const dynamic_modint& x) { return os << x.val(); } } // namespace atcoder #include #include #include template struct Matrix { std::vector> A; Matrix(size_t n, size_t m) : A(n, std::vector(m, 0)) {} Matrix(size_t n) : A(n, std::vector(n, 0)) {} size_t size() const { return A.size(); } size_t height() const { return A.size(); } size_t width() const { return A[0].size(); } inline const std::vector& operator[](int k) const { return A[k]; } inline std::vector& operator[](int k) { return A[k]; } static Matrix I(size_t n) { Matrix res(n); for (size_t i = 0; i < n; i++) res[i][i] = 1; return res; } Matrix& operator+=(const Matrix& B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (size_t i = 0; i < n; i++) { for (size_t 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 (size_t i = 0; i < n; i++) { for (size_t 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()); std::vector> C(n, std::vector(m, 0)); for (size_t i = 0; i < n; i++) { for (size_t k = 0; k < p; k++) { for (size_t j = 0; j < m; j++) { C[i][j] += (*this)[i][k] * B[k][j]; } } } A.swap(C); return *this; } Matrix& operator*=(const T& v) { for (size_t i = 0; i < height(); i++) { for (size_t j = 0; j < width(); j++) { (*this)[i][j] *= v; } } return *this; } Matrix& operator/=(const T& v) { T inv = T(1) / v; for (size_t i = 0; i < height(); i++) { for (size_t j = 0; j < width(); j++) { (*this)[i][j] *= inv; } } return *this; } Matrix& operator^=(long long k) { assert(0 <= k); Matrix B = Matrix::I(size()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1; } A.swap(B.A); return *this; } Matrix operator-() const { Matrix res(height(), width()); for (size_t i = 0; i < height(); i++) { for (size_t j = 0; j < width(); j++) { res[i][j] = -(*this)[i][j]; } } return res; } 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 T& v) const { return Matrix(*this) *= v; } Matrix operator/(const T& v) const { return Matrix(*this) /= v; } Matrix operator^(const long long k) const { return Matrix(*this) ^= k; } bool operator==(const Matrix& B) const { assert(height() == B.height() && width() == B.width()); return A == B.A; } bool operator!=(const Matrix& B) const { assert(height() == B.height() && width() == B.width()); return A != B.A; } Matrix transpose() const { Matrix res(width(), height()); for (size_t i = 0; i < height(); i++) { for (size_t j = 0; j < width(); j++) { res[j][i] = (*this)[i][j]; } } return res; } T determinant() const { assert(height() == width()); Matrix B(*this); T res = 1; for (size_t i = 0; i < height(); i++) { int pivot = -1; for (size_t j = i; j < height(); j++) { if (B[j][i] != 0) { pivot = j; break; } } if (pivot == -1) return 0; if (pivot != (int)i) { res *= -1; std::swap(B[i], B[pivot]); } res *= B[i][i]; T inv = T(1) / B[i][i]; for (size_t j = 0; j < width(); j++) B[i][j] *= inv; for (size_t j = i + 1; j < height(); j++) { T a = B[j][i]; for (size_t k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return res; } friend std::ostream& operator<<(std::ostream& os, const Matrix& p) { size_t n = p.height(), m = p.width(); os << "[(" << n << " * " << m << " Matrix)"; os << "\n[columun sums: "; for (size_t j = 0; j < m; j++) { T sum = 0; for (size_t i = 0; i < n; i++) sum += p[i][j]; ; os << sum << (j + 1 < m ? "," : ""); } os << "]"; for (size_t i = 0; i < n; i++) { os << "\n["; for (size_t j = 0; j < m; j++) os << p[i][j] << (j + 1 < m ? "," : ""); os << "]"; } os << "]\n"; return os; } }; const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; using mint = atcoder::modint1000000007; int main() { cin.tie(0); ios::sync_with_stdio(false); ll L; int N, M; cin >> L >> N >> M; vector K(N, false); for (; M--;) { int k; cin >> k; K[--k] = true; } auto idx = [&](int i, int j, int k) { // i が直近で j 個並んでいて既に良い数列かどうかのフラグが k return i * (N + 1) * 2 + j * 2 + k; }; Matrix m(N * (N + 1) * 2 + 1); for (int i = 0; i < N; i++) { for (int j = 0; j <= N; j++) { for (int k = 0; k < 2; k++) { for (int ni = 0; ni < N; ni++) { int nj = (i == ni ? min(i + 1, j + 1) : 0); int nk = k | (K[i] and j == i and ni != i); m[idx(i, j, k)][idx(ni, nj, nk)]++; } } } } for (int i = 0; i < N; i++) m[idx(N, 0, 0)][idx(i, 0, 0)]++; m ^= L; mint ans = 0; for (int i = 0; i < N; i++) { for (int j = 0; j <= N; j++) { for (int k = 0; k < 2; k++) { mint val = m[idx(N, 0, 0)][idx(i, j, k)]; if (k == 1 or (K[i] and i == j)) ans += val; } } } cout << ans << '\n'; return 0; }