#include #include #include #include #include #include #include #include #include static const int MOD = 1000000007; using ll = int64_t; using u32 = uint32_t; using namespace std; template constexpr T INF = ::numeric_limits::max()/32*15+208; template T extgcd(T a, T b, T &x ,T &y){ for (T u = y = 1, v = x = 0; a; ) { ll q = b/a; swap(x -= q*u, u); swap(y -= q*v, v); swap(b -= q*a, a); } return b; } template T mod_inv(T x, T m){ T s, t; extgcd(x, m, s, t); return (m+s)% m; } #include namespace FFT { const int max_base = 18, maxN = 1 << max_base; // N <= 5e5 const double PI = acos(-1); struct num { double x{}, y{}; num() = default; num(double x, double y): x(x), y(y) {} explicit num(double r): x(cos(r)), y(sin(r)) {} }; num operator+(num a, num b) { return {a.x + b.x, a.y + b.y}; } num operator-(num a, num b) { return {a.x - b.x, a.y - b.y}; } num operator*(num a, num b) { return {a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x}; } num conj(num a) {return {a.x, -a.y}; } num root[maxN]; int rev[maxN]; bool is_root_prepared = false; void prepare_root(){ if(is_root_prepared) return; is_root_prepared = true; root[1] = num(1, 0); for (int i = 1; i < max_base; ++i) { num x(2*PI / (1LL << (i+1))); for (ll j = (1LL << (i-1)); j < (1LL << (i)); ++j) { root[2*j] = root[j]; root[2*j+1] = root[j]*x; } } } int base, N; int lastN = -1; void prepare_rev(){ if(lastN == N) return; lastN = N; for (int i = 0; i < N; ++i) rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (base - 1)); } void fft(num *a, num *f){ for (int i = 0; i < N; ++i) f[i] = a[rev[i]]; for (int k = 1; k < N; k <<= 1) { for (int i = 0; i < N; i += 2*k) { for (int j = 0; j < k; ++j) { num z = f[i+j+k]* root[j+k]; f[i+j+k] = f[i+j] - z; f[i+j] = f[i+j] + z; } } } } num a[maxN], b[maxN], c[maxN], f1[maxN], f2[maxN], f3[maxN]; ll A[maxN], B[maxN], C[maxN]; constexpr ll mask1 = (1LL << 11)-1, mask2 = (1LL << 22)-(1LL << 11), mask3 = (1LL << 33) - (1LL << 22); void multi_mod(int m){ for (int i = 0; i < N; ++i) { a[i] = num( A[i] & mask1, (A[i] & mask2) >> 11); } for (int i = 0; i < N; ++i) { b[i] = num( B[i] & mask1, (B[i] & mask2) >> 11); } for (int i = 0; i < N; ++i) { c[i] = num((A[i] & mask3) >> 22, (B[i] & mask3) >> 22); } fft(a, f1); fft(b, f2); fft(c, f3); for (int i = 0; i < N; ++i) { int j = (N-i)&(N-1); num a1 = (f1[i] + conj(f1[j])) * num(0.5, 0); num a2 = (f1[i] - conj(f1[j])) * num(0, -0.5); num a3 = (f3[i] + conj(f3[j])) * num(0.5, 0); num b1 = (f2[i] + conj(f2[j])) * num(0.5/N, 0); num b2 = (f2[i] - conj(f2[j])) * num(0, -0.5/N); num b3 = (f3[i] - conj(f3[j])) * num(0, -0.5/N); a[j] = a1*b1 + (a1*b2 + a2*b1) * num(0, 1); b[j] = (a1*b3 + a2*b2 + a3*b1) + (a2*b3 + a3*b2) * num(0, 1); c[j] = a3*b3; } fft(a, f1); fft(b, f2); fft(c, f3); for (int i = 0; i < N; ++i) { ll k1 = f1[i].x + 0.5; ll k2 = f1[i].y + 0.5; ll k3 = f2[i].x + 0.5; ll k4 = f2[i].y + 0.5; ll k5 = f3[i].x + 0.5; C[i] = (k1 + ((k2 + ((k3 + ((k4 + (k5 << 11) % m) << 11) % m) << 11) % m) << 11)) % m; } } void prepare_AB(int n1, int n2){ base = 1; N = 2; while(N < n1+n2) base++, N <<= 1; for (int i = n1; i < N; ++i) A[i] = 0; for (int i = n2; i < N; ++i) B[i] = 0; prepare_root(); prepare_rev(); } void multi_mod(int n1, int n2, int m){ prepare_AB(n1, n2); multi_mod(m); } } struct poly { vector v; poly() = default; explicit poly(vector vv) : v(std::move(vv)) {}; int size() const {return (int)v.size(); } poly cut(int len){ if(len < v.size()) v.resize(static_cast(len)); return *this; } inline int& operator[] (int i) {return v[i]; } poly inv() const { int n = size(); vector rr(1, mod_inv(this->v[0], MOD)); poly r(rr); for (int k = 2; k <= n; k <<= 1) { vector u(k); for (int i = 0; i < k; ++i) { u[i] = this->v[i]; } poly ff(u); poly nr = (r*r); nr = nr*ff; nr.cut(k); for (int i = 0; i < k/2; ++i) { nr[i] = (2*r[i]-nr[i]+MOD)%MOD; nr[i+k/2] = (MOD-nr[i+k/2])%MOD; } r = nr; } r.v.resize(n); return r; } poly operator+(const poly &a) const { return poly(*this) += a; } poly operator-(const poly &a) const { return poly(*this) -= a; } poly operator*(const poly &a) const { return poly(*this) *= a; } poly operator/(const poly &a) const { return poly(*this) /= a; } poly& operator+=(const poly &a) { this->v.resize(max(size(), a.size())); for (int i = 0; i < a.size(); ++i) { (this->v[i] += a.v[i]); if(this->v[i] > MOD) this->v[i] -= MOD; } return *this; } poly& operator-=(const poly &a) { this->v.resize(max(size(), a.size())); for (int i = 0; i < a.size(); ++i) { (this->v[i] += MOD-a.v[i]); if(this->v[i] > MOD) this->v[i] -= MOD; } return *this; } poly& operator*=(const poly &a) { for (int i = 0; i < size(); ++i) FFT::A[i] = this->v[i]; for (int i = 0; i < a.size(); ++i) FFT::B[i] = a.v[i]; FFT::multi_mod(size(), a.size(), MOD); this->v.resize(size() + a.size()-1); for (int i = 0; i < size(); ++i) this->v[i] = FFT::C[i]; return *this; } poly& operator/=(const poly &a){ return (*this *= a.inv()); } }; int main() { int k, n; cin >> k >> n; int maxi = 0; vector v(n); for (auto &&i : v) { scanf("%d", &i); maxi = max(maxi, i); } vector p(1<<17, 0); for (int i = 0; i < n; ++i) { p[v[i]] = MOD-1; } p[0] = 1; poly pp(p); poly ppinv = pp.inv(); cout << ppinv[k] << "\n"; return 0; }