#include #include namespace my{ void main(); void solve(); } int main(){my::main();} namespace my{ #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=0;ij>(istream&i,ulll&x){ull t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<>(istream&i,lll&x){ll t;i>>t;x=t;return i;} ostream&operator<<(ostream&o,const lll&x){return o<0?x:-x);} auto range(bool s,ll a,ll b=1e18,ll c=1){if(b==1e18)b=a,(s?b:a)=0;return array{a-s,b,c};} constexpr char nl=10; constexpr char sp=32; lll pw(lll x,ll n,ll m=0){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,m?r%=m,x%=m:r,n>>=1;return r;} bool in(auto l,auto m,auto r){return l<=m&&mauto max(const A&...a){return max(initializer_list>{a...});} templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} bool operator==(const pair&p)const{return a==p.a&&b==p.b;} auto operator<=>(const pair&p)const{return a!=p.a?a<=>p.a:b<=>p.b;} friend ostream&operator<<(ostream&o,const pair&p){return o<>auto&sort(auto&a,const F&f={}){ranges::sort(a,f);return a;} auto pop_back(auto&a){assert(a.size());auto r=*a.rbegin();a.pop_back();return r;} templateostream&operator<<(ostream&o,const std::pair&p){return o<ostream&operator<<(ostream&o,const unordered_map&m){fe(m,e)o<concept vectorial=is_base_of_v,V>; templatestruct core_type{using type=T;}; templatestruct core_type{using type=typename core_type::type;}; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){fe(v,e)o<?nl:sp);return o;} templatestruct vec:vector{ using vector::vector; vec(const vector&v){this->reserve(v.size());fe(v,e)this->eb(e);} vec&operator+=(const vec&u){vec&v=*this;fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;fo(i,v.size())v[i]-=u[i];return v;} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator+(const vec&u)const{return vec{*this}+=u;} vec operator-(const vec&u)const{return vec{*this}-=u;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;} auto scan(const auto&f)const{pair::type,bool>r{};fe(*this,e)if constexpr(!vectorial)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;return r;} auto max()const{return scan([](auto&a,const auto&b){astruct infinity{ templateconstexpr operator T()const{return numeric_limits::max()*(1-is_negative*2);} templateconstexpr operator T()const{return static_cast(*this);} templateconstexpr bool operator==(T x)const{return static_cast(*this)==x;} constexpr auto operator-()const{return infinity();} templateconstexpr operator pair()const{return pair{*this,*this};} }; constexpr infinity oo; void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<>...>>a);} templatevoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<auto rle(const vec&a){vec>r;fe(a,e)r.size()&&e==r.back().a?++r.back().b:r.eb(e,1).b;return r;} templateauto rce(veca){return rle(sort(a));} struct montgomery64{ using i64=__int64_t; using u64=__uint64_t; using u128=__uint128_t; static inline u64 N=998244353; static inline u64 N_inv; static inline u64 R2; static void set_mod(u64 N){ assert(N<(1ULL<<63)); assert(N&1); montgomery64::N=N; R2=-u128(N)%N; N_inv=N; fo(5)N_inv*=2-N*N_inv; assert(N*N_inv==1); } static u64 mod(){ return N; } u64 a; montgomery64(const i64&a=0):a(reduce((u128)(a%(i64)N+N)*R2)){} static u64 reduce(const u128&T){ u128 r=(T+u128(u64(T)*-N_inv)*N)>>64; return r>=N?r-N:r; } auto&operator+=(const montgomery64&b){if((a+=b.a)>=N)a-=N;return*this;} auto&operator-=(const montgomery64&b){if(i64(a-=b.a)<0)a+=N;return*this;} auto&operator*=(const montgomery64&b){a=reduce(u128(a)*b.a);return*this;} auto&operator/=(const montgomery64&b){*this*=b.inv();return*this;} auto operator+(const montgomery64&b)const{return montgomery64(*this)+=b;} auto operator-(const montgomery64&b)const{return montgomery64(*this)-=b;} auto operator*(const montgomery64&b)const{return montgomery64(*this)*=b;} auto operator/(const montgomery64&b)const{return montgomery64(*this)/=b;} bool operator==(const montgomery64&b)const{return a==b.a;} auto operator-()const{return montgomery64()-montgomery64(*this);} montgomery64 pow(u128 n)const{ montgomery64 r{1},x{*this}; while(n){ if(n&1)r*=x; x*=x; n>>=1; } return r; } montgomery64 inv()const{ u64 a=this->a,b=N,u=1,v=0; while(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b); return u; } u64 val()const{ return reduce(a); } friend istream&operator>>(istream&i,montgomery64&b){ ll t;i>>t;b=t; return i; } friend ostream&operator<<(ostream&o,const montgomery64&b){ return o<>9;ll t=a;return lbool miller_rabin(ll n,vecas){ ll d=n-1; while(~d&1)d>>=1; if(modular::mod()!=n)modular::set_mod(n); modular one=1,minus_one=n-1; fe(as,a){ if(a%n==0)continue; ll t=d; modular y=modular(a).pow(t); while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1; if(y!=minus_one&&~t&1)return 0; } return 1; } bool is_prime(ll n){ if(~n&1)return n==2; if(n<=1)return 0; if(n<4759123141LL)return miller_rabin(n,{2,7,61}); return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022}); } templatell pollard_rho(ll n){ if(~n&1)return 2; if(is_prime(n))return n; if(modular::mod()!=n)modular::set_mod(n); modular R,one=1; auto f=[&](const modular&x){return x*x+R;}; while(1){ modular x,y,ys,q=one; R=rand(2,n),y=rand(2,n); ll g=1; constexpr ll m=128; for(ll r=1;g==1;r<<=1){ x=y; fo(r)y=f(y); for(ll k=0;g==1&&k{}; ll d=pollard_rho(m); return d==m?vec{d}:f(f,d)^f(f,m/d); }; return rce(f(f,n)); } templateT mod(T a,T m){return(a%=m)<0?a+m:a;} templateT gcd(T a,T b){return b?gcd(b,a%b):a;} templateauto gcd(const A&...a){common_type_tr=0;((r=gcd(r,a)),...);return r;} templatepairax_by_g(T a,T b){ if(b==0)return{1,0}; auto[s,t]=ax_by_g(b,a%b); return{t,s-a/b*t}; } ll inv_mod(ll a,ll m){ assert(gcd(a,m)==1); auto[x,y]=ax_by_g(a,m); return mod(x,m); } templateT chinese_remainder_theorem_coprime(const vec&a,vec&m,T M=0){ ll K=a.size(); m.eb(M); vect(K),S(K+1),P(K+1,1); fo(i,K){ t[i]=mod((a[i]-S[i])*inv_mod(P[i],m[i]),m[i]); fo(j,i+1,K+1){ S[j]+=t[i]*P[j]; P[j]*=m[i]; if(m[j])S[j]%=m[j],P[j]%=m[j]; } } ll r=S.back(); m.pop_back(); return S.back(); } templateT chinese_remainder_theorem(const vec&a,const vec&m,T M=0){ ll K=a.size(); fo(i,K)fo(j,i+1,K)if((a[i]-a[j])%gcd(m[i],m[j]))return-1; unordered_map>exponent_max_congruence; fo(i,K)fe(factorize(m[i]),p,b)if(exponent_max_congruence[p].ba_mod_prime_pow,m_mod_prime_pow; fe(exponent_max_congruence,p,v){ T pq=pw(p,v.b); a_mod_prime_pow.eb(v.a%pq); m_mod_prime_pow.eb(pq); } return chinese_remainder_theorem_coprime(a_mod_prime_pow,m_mod_prime_pow,M); } void main(){io();ll T=1;fo(T)solve();} void solve(){ LL(N,K); veca(K);lin(a); vecr(2); vecM{168647939,592951213}; ll N2=(N+1)/2; vecdp; fo(f,2){ dp.assign(N2,0); dp[0]=1; fo(i,N2){ fo(j,K)if(i+a[j]