#include using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector< C > rts = {{0, 0}, {1, 0}}; vector< int > rev = {0, 1}; void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while(base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector< C > &a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) { int need = (int) a.size() + (int) b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < sz; i++) { int x = (i < (int) a.size() ? a[i] : 0); int y = (i < (int) b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for(int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector< int64_t > ret(need); for(int i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } }; template< typename T > struct ArbitraryModConvolution { using real = FastFourierTransform::real; using C = FastFourierTransform::C; ArbitraryModConvolution() = default; vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) { if(need == -1) need = a.size() + b.size() - 1; int nbase = 0; while((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < a.size(); i++) { fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15); } fft(fa, sz); vector< C > fb(sz); if(a == b) { fb = fa; } else { for(int i = 0; i < b.size(); i++) { fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15); } fft(fb, sz); } real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if(i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector< T > ret(need); for(int i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa).x, bb = T(bb).x, cc = T(cc).x; ret[i] = aa + (bb << 15) + (cc << 30); } return ret; } }; template< typename T > struct PolynominalMod : vector< T > { using vector< T >::vector; using P = PolynominalMod; static ArbitraryModConvolution< T > fft; P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } P operator/(const P &r) const { return P(*this) /= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i]; return *this; } P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } auto ret = fft.multiply(*this, r); this->resize(ret.size()); for(int k = 0; k < ret.size(); k++) (*this)[k] = ret[k]; return *this; } P operator-() const { P ret(this->size()); for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator/=(const P &r) { return *this *= r.inverse(); } P inverse() const { const int n = (int) this->size(); assert(n); P ret({T(1) / (*this)[0]}); for(int k = 2; (k >> 1) < n; k <<= 1) { P ff(min(n, k)); for(int i = 0; i < ff.size(); i++) ff[i] = (*this)[i]; P nr = ret * ret; nr.resize(ff.size()); nr = nr * ff; nr.resize(ff.size()); for(int i = 0; i < (k >> 1); i++) nr[i] -= ret[i] + ret[i]; ret = -nr; } return ret; } }; int main() { int K, N; cin >> K >> N; PolynominalMod< modint > X(K + 1); X[0] = 1; for(int i = 0; i < N; i++) { int x; cin >> x; if(x <= K) X[x] = -1; } cout << X.inverse()[K] << endl; }