#include #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(i, n) for (ll i = 0; i < ll(n); ++i) #define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--) #define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--) #define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d) #define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define SUM(a) accumulate(all(a),0LL) #define MIN(a) *min_element(all(a)) #define MAX(a) *max_element(all(a)) #define SORT(a) sort(all(a)); #define REV(a) reverse(all(a)); #define SZ(a) int(a.size()) #define popcount(x) __builtin_popcountll(x) #define pf push_front #define pb push_back #define ef emplace_front #define eb emplace_back #define ppf pop_front #define ppb pop_back #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0); #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using ll = long long; using ld = long double; using P = pair; using LP = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vd = vector; using vvd = vector; using vs = vector; using vc = vector; using vvc = vector; using vb = vector; using vvb = vector; using vp = vector

; using vvp = vector; template using PQ = priority_queue, vector>, greater>>; template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << '{' << p.first << ", " << p.second << '}'; } template istream &operator>>(istream &is, tuple &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); } template ostream &operator<<(ostream &os, const tuple &t) { return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}'; } template istream &operator>>(istream &is, vector &v) { for (T &t: v) { is >> t; } return is; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const deque &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const set &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template ostream &operator<<(ostream &os, const multiset &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template void vecout(const vector &v, char div = '\n') { rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div); } template bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } void scan() {} template void scan(Head &head, Tail &... tail) { cin >> head; scan(tail...); } template void print(const T &t) { cout << t << '\n'; } template void print(const Head &head, const Tail &... tail) { cout << head << ' '; print(tail...); } template void fin(const T &... a) { print(a...); exit(0); } template vector &operator+=(vector &v, T x) { for (T &t: v) t += x; return v; } template vector &operator-=(vector &v, T x) { for (T &t: v) t -= x; return v; } template vector &operator*=(vector &v, T x) { for (T &t: v) t *= x; return v; } template vector &operator/=(vector &v, T x) { for (T &t: v) t /= x; return v; } struct Init_io { Init_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout << boolalpha << fixed << setprecision(15); cerr << boolalpha << fixed << setprecision(15); } } init_io; const string yes[] = {"no", "yes"}; const string Yes[] = {"No", "Yes"}; const string YES[] = {"NO", "YES"}; const int inf = 1001001001; const ll linf = 1001001001001001001; void rearrange(const vi &) {} template void rearrange(const vi &ord, vector &head, Tail &...tail) { assert(ord.size() == head.size()); vector ori = head; rep(i, ord.size()) head[i] = ori[ord[i]]; rearrange(ord, tail...); } template void sort_by(vector &head, Tail &... tail) { vi ord(head.size()); iota(all(ord), 0); sort(all(ord), [&](int i, int j) { return head[i] < head[j]; }); rearrange(ord, head, tail...); } template vector cumsum(const vector &v, bool shift_one = true) { int n = v.size(); vector res; if (shift_one) { res.resize(n + 1); rep(i, n) res[i + 1] = res[i] + v[i]; } else { res.resize(n); if (n) { res[0] = v[0]; rep(i, 1, n) res[i] = res[i - 1] + v[i]; } } return res; } vvi graph(int n, int m, bool directed = false, int origin = 1) { vvi G(n); rep(_, m) { INT(u, v); u -= origin, v -= origin; G[u].pb(v); if (!directed) G[v].pb(u); } return G; } template vector>> weighted_graph(int n, int m, bool directed = false, int origin = 1) { vector>> G(n); rep(_, m) { int u, v; T w; scan(u, v, w); u -= origin, v -= origin; G[u].eb(v, w); if (!directed) G[v].eb(u, w); } return G; } template class modint { ll x; public: constexpr modint(ll x = 0) : x((x % mod + mod) % mod) {} static constexpr int get_mod() { return mod; } constexpr int val() const { return x; } constexpr modint operator-() const { return modint(-x); } constexpr modint &operator+=(const modint &a) { if ((x += a.val()) >= mod) x -= mod; return *this; } constexpr modint &operator++() { return *this += 1; } constexpr modint &operator-=(const modint &a) { if ((x += mod - a.val()) >= mod) x -= mod; return *this; } constexpr modint &operator--() { return *this -= 1; } constexpr modint &operator*=(const modint &a) { (x *= a.val()) %= mod; return *this; } constexpr modint operator+(const modint &a) const { modint res(*this); return res += a; } constexpr modint operator-(const modint &a) const { modint res(*this); return res -= a; } constexpr modint operator*(const modint &a) const { modint res(*this); return res *= a; } constexpr modint pow(ll t) const { modint res = 1, a(*this); while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } template friend istream &operator>>(istream &, modint &); // for prime mod constexpr modint inv() const { return pow(mod - 2); } constexpr modint &operator/=(const modint &a) { return *this *= a.inv(); } constexpr modint operator/(const modint &a) const { modint res(*this); return res /= a; } }; using modint998244353 = modint<998244353>; using modint1000000007 = modint<1000000007>; template istream &operator>>(istream &is, modint &a) { return is >> a.x; } template constexpr ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } template constexpr bool operator==(const modint &a, const modint &b) { return a.val() == b.val(); } template constexpr bool operator!=(const modint &a, const modint &b) { return a.val() != b.val(); } template constexpr modint &operator++(modint &a) { return a += 1; } template constexpr modint &operator--(modint &a) { return a -= 1; } using mint = modint1000000007; using vm = vector; using vvm = vector; template class matrix : public vector> { public: using vector>::vector; constexpr int get_h() const { return this->size(); } constexpr int get_w() const { return (get_h() ? (*this)[0].size() : 0); } constexpr matrix &operator+=(const matrix &a) { rep(i, get_h()) rep(j, get_w()) (*this)[i][j] += a[i][j]; return *this; } constexpr matrix &operator*=(const int &k) { rep(i, get_h()) rep(j, get_w()) (*this)[i][j] *= k; return *this; } constexpr matrix &operator-=(const matrix &a) { *this += a * (-1); return *this; } constexpr matrix operator+(const matrix &a) const { return res(*this) += a; } constexpr matrix operator*(const int &k) const { return res(*this) *= k; } constexpr matrix operator-(const matrix &a) const { return res(*this) -= a; } constexpr matrix operator*(const matrix &a) const { int h = get_h(), w = get_w(), ah = a.get_h(), aw = a.get_w(); assert(w == ah); matrix res(h, vector(aw)); rep(i, h) rep(j, w) rep(k, aw) res[i][k] += (*this)[i][j] * a[j][k]; return res; } constexpr matrix &operator*=(const matrix &a) { return *this = *this * a; } constexpr matrix pow(ll t) const { int h = get_h(), w = get_w(); assert(h == w); matrix res(h, vector(w)), a(*this); rep(i, get_h()) res[i][i] = 1; while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } }; using mat = matrix; int main() { LL(l); INT(n, m); vi k(m); scan(k); vi used(n + 1); rep(i, m) used[k[i]] = true; vi ofs(n + 2); rep(i, 1, n + 1) { ofs[i + 1] = ofs[i] + (used[i] ? i + 1 : 1); } int sz = ofs.back() + 2; mat init(sz, vm(1)); rep(i, 1, n + 1) { if (used[i] and i == 1) init[sz - 1][0] += 1; init[ofs[i]][0] += 1; } mat trans(sz, vm(sz)); rep(i, 1, n + 1) { int num = (used[i] ? i + 1 : 1); rep(j, num) { int now = ofs[i] + j; if (j < num - 1) trans[now + 1][now] += 1; else trans[now][now] += 1; if (j == num - 3) trans[sz - 1][now] += 1; if (j == num - 2) continue; rep(ni, 1, n + 1) { if (i == ni) continue; if (used[ni] and ni == 1) trans[sz - 1][now] += 1; trans[ofs[ni]][now] += 1; } } } trans[sz - 2][sz - 1] += n - 1; trans[sz - 2][sz - 2] += n; mat ans = trans.pow(l - 1) * init; fin(ans[sz - 2][0] + ans[sz - 1][0]); }