/** * code generated by JHelper * More info: https://github.com/AlexeyDmitriev/JHelper * @author */ #include using namespace std; using ll = long long; //#pragma GCC optimize("O3") //#pragma GCC target("avx2") //#pragma GCC optimize("unroll-loops") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") //#pragma GCC optimize("Ofast") #define VI vector #define G(size_1) vector>(size_1, vector()) #define SZ(x) ((int)(x).size()) #define READ ({int t;cin >> t;t;}) #define PII pair #define FOR(i, _begin, _end) for (__typeof(_end) end = _end, begin = _begin, i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end))) #define REP(i, end) for (__typeof(end) i = 0, _len = (end); i < (_len); i += 1) #define ALL(x) (x).begin(),(x).end() #define RALL(x) (x).rbegin(),(x).rend() #define F first #define S second #define y0 y3487465 #define y1 y8687969 #define j0 j1347829 #define j1 j234892 #define MOD(x, m) ((((x) % (m)) + (m)) % (m)) #define BIT(n) (1LL<<(n)) #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define EB emplace_back #define PB push_back #define fcout cout << fixed << setprecision(12) #define fcerr cerr << fixed << setprecision(12) #define print(x) cout << (x) << '\n' #define printE(x) cout << (x) << endl #define fprint(x) cout << fixed << setprecision(12) << (x) << endl # define BYE(a) do { cout << (a) << endl; return ; } while (false) #ifdef DEBUG #define DBG(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator _it(_ss); _err(cerr,_it, args); } #define ERR(x) std::cerr << #x << " = " << x << endl; #else #define DBG(x) {}; #define ERR(args...) {}; #endif void _err(std::ostream& cerr,istream_iterator it) {cerr << endl;} template void _err(std::ostream& cerr, istream_iterator it, T a, Args... args) { cerr << *it << " = " << a << " "; _err(cerr,++it, args...); } const double pi = 2 * acos(.0); const int inf = 0x3f3f3f3f; const ll mod = (ll) (1e9) + 7; templatebool Chmax(T &a, const T &b) { if (abool Chmin(T &a, const T &b) { if (b istream& operator >> (istream& is, vector& V) { for(auto&& ele : V)is >> ele; return is; } template ostream& operator << (ostream& os, const vector V) { os << "["; int cnt = 0; T curr; if(!V.empty()){ for (int i = 0; i < V.size() - 1; ++i) { if(V[i] == curr)cnt ++; else cnt = 0; if(cnt == 4)os << "... "; if(cnt < 4) os << i << ":" << V[i] << " "; curr = V[i]; } os << V.size() - 1 << ":" << V.back(); } os << "]\n"; return os; } template ostream& operator << (ostream& os, const pair P) { os << "("; os << P.first << "," << P.second; os << ")"; return os; } template ostream& operator << (ostream& os, const set V) { os << "{"; if(!V.empty()){ auto it = V.begin(); for (int i = 0; i < V.size() -1; ++i) { os << *it << " "; it++; } os << *it; } os << "}\n"; return os; } template ostream& operator << (ostream& os, const unordered_set V) { os << "{"; if(!V.empty()){ auto it = V.begin(); for (int i = 0; i < V.size() -1; ++i) { os << *it << " "; it++; } os << *it; } os << "}\n"; return os; } template ostream& operator << (ostream& os, const multiset V) { os << "{"; if(!V.empty()){ auto it = V.begin(); for (int i = 0; i < V.size() -1; ++i) { os << *it << " "; it++; } os << *it; } os << "}"; return os; } template ostream& operator << (ostream& os, const map V) { os << "{"; if(!V.empty()){ auto it = V.begin(); for (int i = 0; i < V.size() -1; ++i) { os << "("; os << it->first << "," << it->second; os << ") "; it++; } os << "("; os << it->first << "," << it->second; os << ")"; } os << "}\n"; return os; } template ostream& operator << (ostream& os, const unordered_map V) { os << "{"; if(!V.empty()){ auto it = V.begin(); for (int i = 0; i < V.size() -1; ++i) { os << "("; os << it->first << "," << it->second; os << ") "; it++; } os << "("; os << it->first << "," << it->second; os << ")"; } os << "}\n"; return os; } template ostream& operator << (ostream& os, const deque V) { os << "["; if (!V.empty()) { for (int i = 0; i < V.size() - 1; ++i) { os << V[i] << "->"; } if (!V.empty())os << V.back(); } os << "]\n"; return os; }; template ostream& operator << (ostream& os, const priority_queue V) { priority_queue _V = V; os << "["; if(!_V.empty()){ while(_V.size() > 1){ os << _V.top() << "->"; _V.pop(); } os << _V.top(); } os << "]\n"; return os; }; template struct y_combinator { F f; // the lambda will be stored here // a forwarding operator(): template decltype(auto) operator()(Args&&... args) const { // we pass ourselves to f, then the arguments. // the lambda should take the first argument as `auto&& recurse` or similar. return f(*this, std::forward(args)...); } }; // helper function that deduces the type of the lambda: template y_combinator> recursive(F&& f){ return {std::forward(f)}; } struct hash_pair { template size_t operator()(const pair& p) const { auto hash1 = hash{}(p.first); auto hash2 = hash{}(p.second); return hash1 ^ hash2; } }; template std::vector multi_vector(int n, U v) { return std::vector(n, v); } template auto multi_vector(int n, Args... args) { auto val = multi_vector(std::forward(args)...); return std::vector(n, std::move(val)); } template struct mod_int { constexpr static signed MODULO = M; constexpr static unsigned TABLE_SIZE = T; signed x; mod_int() : x(0) {} mod_int(long long y) : x(static_cast(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {} mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {} explicit operator int() const { return x; } explicit operator long long() const { return x; } explicit operator double() const { return x; } mod_int &operator+=(const mod_int &rhs) { if ((x += rhs.x) >= MODULO) x -= MODULO; return *this; } mod_int &operator-=(const mod_int &rhs) { if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO; return *this; } mod_int &operator*=(const mod_int &rhs) { x = static_cast(1LL * x * rhs.x % MODULO); return *this; } mod_int &operator/=(const mod_int &rhs) { x = static_cast((1LL * x * rhs.inv().x) % MODULO); return *this; } mod_int operator-() const { return mod_int(-x); } mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; } mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; } mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; } mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; } bool operator<(const mod_int &rhs) const { return x < rhs.x; } mod_int inv() const { assert(x != 0); if (x <= static_cast(TABLE_SIZE)) { if (_inv[1].x == 0) prepare(); return _inv[x]; } else { signed a = x, b = MODULO, u = 1, v = 0, t; while (b) { t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } return mod_int(u); } } mod_int pow(long long t) const { assert(!(x == 0 && t == 0)); mod_int e = *this, res = mod_int(1); for (; t; e *= e, t >>= 1) if (t & 1) res *= e; return res; } mod_int fact() { if (_fact[0].x == 0) prepare(); return _fact[x]; } mod_int inv_fact() { if (_fact[0].x == 0) prepare(); return _inv_fact[x]; } mod_int choose(mod_int y) { assert(y.x <= x); return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact(); } static mod_int _inv[TABLE_SIZE + 1]; static mod_int _fact[TABLE_SIZE + 1]; static mod_int _inv_fact[TABLE_SIZE + 1]; static void prepare() { _inv[1] = 1; for (int i = 2; i <= (int)TABLE_SIZE; ++i) { _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO; } _fact[0] = 1; for (unsigned i = 1; i <= TABLE_SIZE; ++i) { _fact[i] = _fact[i - 1] * int(i); } _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv(); for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) { _inv_fact[i] = _inv_fact[i + 1] * (i + 1); } } }; template std::ostream &operator<<(std::ostream &os, const mod_int &rhs) { return os << rhs.x; } template std::istream &operator>>(std::istream &is, mod_int &rhs) { long long s; is >> s; rhs = mod_int(s); return is; } template mod_int mod_int::_inv[TABLE_SIZE + 1]; template mod_int mod_int::_fact[TABLE_SIZE + 1]; template mod_int mod_int::_inv_fact[TABLE_SIZE + 1]; template bool operator==(const mod_int &lhs, const mod_int &rhs) { return lhs.x == rhs.x; } template bool operator!=(const mod_int &lhs, const mod_int &rhs) { return !(lhs == rhs); } const int MF = 1000010; const int MOD = 1000000007; using mint = mod_int; mint binom(int n, int r) { return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r); } mint fact(int n) { return mint(n).fact(); } mint inv_fact(int n) { return mint(n).inv_fact(); } class No3046Yukicoder { public: void solve(std::istream& cin, std::ostream& cout, std::ostream& cerr) { int K,N;cin >> K >> N; VI a(N);cin >> a; VI solved(K+1); vector memo(K+1); auto dp = recursive([&](auto &&dp, int n)->mint { if (solved[n])return memo[n]; if (n == 0)return 1; mint ans = 0; int i = 0; while (i < N && n >= a[i])ans += dp(n - a[i]), i++; solved[n] = 1; return memo[n] = ans; }); // std::function dp = [&](int n)->mint { // ERR(n); // if (solved[n])return memo[n]; // if (n == 0)return 1; // mint ans = 0; // int i = 0; // while (i < N && n >= a[i])ans += dp(n - a[i]), i++; // solved[n] = 1; // return memo[n] = ans; // }; print(dp(K)); } }; #undef int int main() { No3046Yukicoder solver; std::istream& in(std::cin); std::ostream& out(std::cout); std::ostringstream err; in.tie(0); ios::sync_with_stdio(0); solver.solve(in, out,err); return 0; }