#include using namespace std; using ll = long long; #define ALL(obj) (obj).begin(),(obj).end() template using priority_queue_reverse = priority_queue,greater>; constexpr long long MOD = 1'000'000'000LL + 7; //' constexpr long long MOD2 = 998244353; constexpr long long HIGHINF = (long long)1e18; constexpr long long LOWINF = (long long)1e15; constexpr long double PI = 3.1415926535897932384626433L; template vector multivector(size_t N,T init){return vector(N,init);} template auto multivector(size_t N,T... t){return vector(N,multivector(t...));} template void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} template ostream &operator<<(ostream &o, const map&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} template ostream &operator<<(ostream &o, const set&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const multiset&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} template ostream &operator<<(ostream &o, const vector&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} template ostream &operator<<(ostream &o, const pair&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} void print(void) {cout << endl;} template void print(Head&& head) {cout << head;print();} template void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward(tail)...);} template void chmax(T& a, const T b){a=max(a,b);} template void chmin(T& a, const T b){a=min(a,b);} vector split(const string &str, const char delemiter) {vector res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;} int msb(int x) {return x?31-__builtin_clz(x):-1;} void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} /* * @title ModInt * @docs md/util/ModInt.md */ template class ModInt { public: long long x; constexpr ModInt():x(0) {} constexpr ModInt(long long 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 long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;} ModInt &operator+=(const int y) {ModInt p(y);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 long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;} ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;} ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;} ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;} ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;} ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;} ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;} ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;} ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;} ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;} ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;} ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;} ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;} ModInt operator-() const {return ModInt(-x); } ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;} ModInt operator--() {x--;if(x<0) x+=mod;return *this;} 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; } 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 inv() 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(long long n) const {ModInt ret(1), mul(x);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;return ret;} friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;} friend istream &operator>>(istream &is, ModInt &a) {long long t;is >> t;a = ModInt(t);return (is);} }; //using modint = ModInt; /* * @title FastFourierTransform - 高速フーリエ変換 * @docs md/math/FastFourierTransform.md */ class FastFourierTransform { inline static constexpr int prime1 =1004535809; inline static constexpr int prime2 =998244353; inline static constexpr int prime3 =985661441; inline static constexpr int inv21 =332747959; // ModInt(mod1).inv().x; inline static constexpr int inv31 =766625513; // ModInt(mod1).inv().x; inline static constexpr int inv32 =657107549; // ModInt(mod2).inv().x; inline static constexpr long long prime12=(1002772198720536577LL); inline static constexpr array pow2 = {1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432}; using Mint1 = ModInt; using Mint2 = ModInt; using Mint3 = ModInt; inline static long long garner(const Mint1& b1,const Mint2& b2,const Mint3& b3) {Mint2 t2 = (b2-b1.x)*inv21;Mint3 t3 = ((b3-b1.x)*inv31-t2.x)*inv32;return prime12*t3.x+b1.x+prime1*t2.x;} template inline static void ntt(vector>& f) { const int N = f.size(), M = N>>1; const int log2_N = __builtin_ctz(N); ModInt h(3); vector> g(N),base(log2_N); for(int i=0;i w = 1; for (int i=0,k=0;i l = f[k|j],r = w*f[k|j|p]; g[i|j] = l + r; g[i|j|M] = l - r; } } swap(f,g); } } template inline static vector> convolution_friendlymod(const vector& a,const vector& b){ if (min(a.size(), b.size()) <= 60) { vector> f(a.size() + b.size() - 1); for (int i = 0; i < a.size(); i++) for (int j = 0; j < b.size(); j++) f[i+j]+=a[i]*b[j]; return f; } int N,M=a.size()+b.size()-1; for(N=1;N inverse(N); inverse = inverse.inv(); vector> g(N,0),h(N,0); for(int i=0;i(g); ntt(h); for(int i = 0; i < N; ++i) g[i] *= h[i]*inverse; reverse(g.begin()+1,g.end()); ntt(g); return g; } public: inline static vector convolution(const vector& g,const vector& h){ auto f1 = convolution_friendlymod(g, h); auto f2 = convolution_friendlymod(g, h); auto f3 = convolution_friendlymod(g, h); vector f(f1.size()); for(int i=0; i> N >> Q; vector A(N),B(N,0),D(N,0); for(int i=0;i> A[i]; while(Q--){ int r; cin >> r; B[N-1-r]++; } auto C = FastFourierTransform::convolution(A,B); for(int i=0;i<2*N-1;++i) { D[(i+1)%N]+=C[i]; } for(int i=0;i