#include using namespace std; #if __has_include() #include using namespace atcoder; templateistream &operator>>(istream &is,static_modint &a){long long b;is>>b;a=b;return is;} istream &operator>>(istream &is,modint &a){long long b;cin>>b;a=b;return is;} #endif #ifdef LOCAL #include "debug.h" #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) templateostream &operator<<(ostream &os,const pair&p){os<; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templateistream &operator>>(istream &is,pair&p){is>>p.first>>p.second;return is;} templateistream &operator>>(istream &is,vector &a){for(auto &i:a)is>>i;return is;} templatevoid operator++(pair&a,int n){a.first++,a.second++;} templatevoid operator--(pair&a,int n){a.first--,a.second--;} templatevoid operator++(vector&a,int n){for(auto &i:a)i++;} templatevoid operator--(vector&a,int n){for(auto &i:a)i--;} #define reps(i,a,n) for(int i=(a);i<(n);i++) #define rep(i,n) reps(i,0,n) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcount(x) ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } void SOLVE(); int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); #ifdef LOCAL clock_t start=clock(); #endif int testcase=1; //cin>>testcase; for(int i=0;i>r,int mod){ r.emplace_back(0,mod); vectora(r.size(),1),b(r.size(),0); rep(i,r.size()-1){ ll v=(r[i].first-b[i])*inv_mod(a[i],r[i].second)%r[i].second; if(v<0)v+=r[i].second; reps(j,i+1,r.size()){ b[j]+=a[j]*v; b[j]%=r[j].second; a[j]*=r[i].second; a[j]%=r[j].second; } } return b[r.size()-1]; } template vectoranymod_convolution(const vector&a,const vector&b){ if(a.empty()||b.empty())return vector{}; if(min(a.size(),b.size())<60){ vectorret(a.size()+b.size()-1,0); rep(i,a.size())rep(j,b.size())ret[i+j]+=a[i]*b[j]; return ret; } using mint1=static_modint<167772161>; using mint2=static_modint<469762049>; using mint3=static_modint<1224736769>; vectora1(a.size()),b1(b.size()); vectora2(a.size()),b2(b.size()); vectora3(a.size()),b3(b.size()); rep(i,a.size()){ a1[i]=a[i].val(); a2[i]=a[i].val(); a3[i]=a[i].val(); } rep(i,b.size()){ b1[i]=b[i].val(); b2[i]=b[i].val(); b3[i]=b[i].val(); } a1=convolution(a1,b1),a2=convolution(a2,b2),a3=convolution(a3,b3); vectorret(a.size()+b.size()-1); rep(i,ret.size()){ vector>r(3); r[0].first=a1[i].val(),r[0].second=mint1::mod(); r[1].first=a2[i].val(),r[1].second=mint2::mod(); r[2].first=a3[i].val(),r[2].second=mint3::mod(); ret[i]=garner(r,T::mod()); } return ret; } using mint=modint1000000007; void SOLVE(){ int k,n; cin>>k>>n; vectorcoef(k+1,0); rep(i,n){ int x; cin>>x; if(x<=k)coef[x]=1; } vectordp(k+1,0); dp[0]=1; auto solve=[&](auto self,int l,int r){ if(l+1==r)return; int mid=(l+r)/2; self(self,l,mid); vectorf{dp.begin()+l,dp.begin()+mid}; vectorg{coef.begin(),coef.begin()+r-l}; vectorc=anymod_convolution(f,g); rep(i,c.size())if(mid<=l+i&&l+i