#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct MInt { unsigned int v; MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {} static constexpr int get_mod() { return M; } static void set_mod(const int divisor) { assert(divisor == M); } static void init(const int x = 10000000) { inv(x, true); fact(x); fact_inv(x); } static MInt inv(const int n, const bool init = false) { // assert(0 <= n && n < M && std::__gcd(n, M) == 1); static std::vector inverse{0, 1}; const int prev = inverse.size(); if (n < prev) { return inverse[n]; } else if (init) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[M % i] * (M / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = M; b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector factorial{1}; const int prev = factorial.size(); if (n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector f_inv{1}; const int prev = f_inv.size(); if (n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) return 0; return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) return 0; inv(k, true); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if ((v += x.v) >= M) v -= M; return *this; } MInt& operator-=(const MInt& x) { if ((v += M - x.v) >= M) v -= M; return *this; } MInt& operator*=(const MInt& x) { v = static_cast(v) * x.v % M; return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } bool operator==(const MInt& x) const { return v == x.v; } bool operator!=(const MInt& x) const { return v != x.v; } bool operator<(const MInt& x) const { return v < x.v; } bool operator<=(const MInt& x) const { return v <= x.v; } bool operator>(const MInt& x) const { return v > x.v; } bool operator>=(const MInt& x) const { return v >= x.v; } MInt& operator++() { if (++v == M) v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? M - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(v ? M - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } }; using ModInt = MInt; template struct Matrix { explicit Matrix(const int m, const int n, const T def = 0) : data(m, std::vector(n, def)) {} int nrow() const { return data.size(); } int ncol() const { return data.front().size(); } Matrix pow(long long exponent) const { const int n = nrow(); Matrix res(n, n, 0), tmp = *this; for (int i = 0; i < n; ++i) { res[i][i] = 1; } for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } inline const std::vector& operator[](const int i) const { return data[i]; } inline std::vector& operator[](const int i) { return data[i]; } Matrix& operator=(const Matrix& x) = default; Matrix& operator+=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] += x[i][j]; } } return *this; } Matrix& operator-=(const Matrix& x) { const int m = nrow(), n = ncol(); for (int i = 0; i < m; ++i) { for (int j = 0; j < n; ++j) { data[i][j] -= x[i][j]; } } return *this; } Matrix& operator*=(const Matrix& x) { const int m = nrow(), l = ncol(), n = x.ncol(); std::vector> res(m, std::vector(n, 0)); for (int i = 0; i < m; ++i) { for (int k = 0; k < l; ++k) { for (int j = 0; j < n; ++j) { res[i][j] += data[i][k] * x[k][j]; } } } data.swap(res); return *this; } Matrix operator+(const Matrix& x) const { return Matrix(*this) += x; } Matrix operator-(const Matrix& x) const { return Matrix(*this) -= x; } Matrix operator*(const Matrix& x) const { return Matrix(*this) *= x; } private: std::vector> data; }; int main() { ll l; int n, m; cin >> l >> n >> m; vector k(m); REP(i, m) cin >> k[i]; vector> v; REP(i, m) FOR(j, 1, k[i] + 2) v.emplace_back(j, k[i]); const int d = v.size(); vector start(n + 1, d); REP(i, d) { if (v[i].first == 1) start[v[i].second] = i; } Matrix a(d + 2, d + 2); REP(i, d) { if (v[i].first > v[i].second) { a[i][i] = 1; FOR(j, 1, n + 1) { if (j != v[i].second) ++a[start[j]][i]; } } else if (v[i].first == v[i].second) { a[i + 1][i] = 1; a[d + 1][i] = n - 1; } else { a[i + 1][i] = 1; FOR(j, 1, n + 1) { if (j != v[i].second) ++a[start[j]][i]; } } } FOR(j, 1, n + 1) ++a[start[j]][d]; a[d + 1][d + 1] = n; a = a.pow(l); ModInt ans = a[d + 1][d]; REP(i, d) { if (v[i].first == v[i].second) ans += a[i][d]; } cout << ans << '\n'; return 0; }