#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC push_options
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define LINF (9223372036854775807LL)
#define EPS (1e-10)
#define endl ('\n')
#define MOD 1000000007LL
//#define MOD 998244353LL
//#define MOD 18446744069414584321ULL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,...) for(auto i:range(__VA_ARGS__)) 
#define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
inline vector<int64_t> range(int64_t n){vector<int64_t>v(n);iota(v.begin(),v.end(),0LL);return v;}
inline vector<int64_t> range(int64_t a,int64_t b){vector<int64_t>v(b-a);iota(v.begin(),v.end(),a);return v;}
inline vector<int64_t> range(int64_t a,int64_t b,int64_t c){vector<int64_t>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
inline auto reversed(auto v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
//inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
//inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
auto call=[](auto f,auto... args){return f(f,args...);};
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}

template<typename T,typename F>
struct FPS_BASE:vector<T>{
    using vector<T>::vector;
    using P=FPS_BASE<T,F>;
    F fft;
    FPS_BASE(){}
    inline P operator +(T x)const noexcept{return P(*this)+=x;}
    inline P operator -(T x)const noexcept{return P(*this)-=x;}
    inline P operator *(T x)const noexcept{return P(*this)*=x;}
    inline P operator /(T x)const noexcept{return P(*this)/=x;}
    inline P operator <<(int x)noexcept{return P(*this)<<=x;}
    inline P operator >>(int x)noexcept{return P(*this)>>=x;}
    inline P operator +(const P& x)const noexcept{return P(*this)+=x;}
    inline P operator -(const P& x)const noexcept{return P(*this)-=x;}
    inline P operator -()const noexcept{return P(1,T(0))-=P(*this);}
    inline P operator *(const P& x)const noexcept{return P(*this)*=x;}
    inline P operator /(const P& x)const noexcept{return P(*this)/=x;}
    inline P operator %(const P& x)const noexcept{return P(*this)%=x;}
    bool operator ==(P x){
        for(int i=0;i<(int)max((*this).size(),x.size());++i){
            if(i>=(int)(*this).size()&&x[i]!=T())return 0;
            if(i>=(int)x.size()&&(*this)[i]!=T())return 0;
            if(i<(int)min((*this).size(),x.size()))if((*this)[i]!=x[i])return 0;
        }
        return 1;
    }
    P &operator +=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*this)[0]+=x;
        return (*this);
    }
    P &operator -=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*this)[0]-=x;
        return (*this);
    }
    P &operator *=(T x){
        for(int i=0;i<(int)this->size();++i){
            (*this)[i]*=x;
        }
        return (*this);
    }
    P &operator /=(T x){
        return (*this)*=(T(1)/x);
    }
    P &operator <<=(int x){
        P ret(x,T(0));
        ret.insert(ret.end(),begin(*this),end(*this));
        return (*this)=ret;
    }
    P &operator >>=(int x){
        P ret;
        ret.insert(ret.end(),begin(*this)+x,end(*this));
        return (*this)=ret;
    }
    P &operator +=(const P& x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*this)[i]+=x[i];
        }
        return (*this);
    }
    P &operator -=(const P& x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*this)[i]-=x[i];
        }
        return (*this);
    }
    P &operator *=(const P& x){
        return (*this)=F()(*this,x);
    }
    P &operator /=(P x){
        if(this->size()<x.size()) {
            this->clear();
            return (*this);
        }
        const int n=this->size()-x.size()+1;
        return (*this) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n);
    }
    P &operator %=(const P& x){
        return ((*this)-=*this/x*x);
    }
    inline void print(){
        for(int i=0;i<(int)(*this).size();++i)cerr<<(*this)[i]<<" \n"[i==(int)(*this).size()-1];
        if((int)(*this).size()==0)cerr<<endl;
    }
    inline P& shrink(){while((*this).back()==0)(*this).pop_back();return (*this);}
    inline P pre(int sz)const{
        return P(begin(*this),begin(*this)+min((int)this->size(),sz));
    }
    P rev(int deg=-1){
        P ret(*this);
        if(deg!=-1)ret.resize(deg,T(0));
        reverse(begin(ret),end(ret));
        return ret;
    }
    P inv(int deg=-1){
        assert((*this)[0]!=T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)/(*this)[0]});
        for(int i=1;i<n;i<<=1){
            ret*=(-ret*pre(i<<1)+2).pre(i<<1);
        }
        return ret.pre(n);
    }
    inline P dot(const P& x){
        P ret(*this);
        for(int i=0;i<int(min(this->size(),x.size()));++i){
            ret[i]*=x[i];
        }
        return ret;
    }
    P diff(){
        if((int)(*this).size()<=1)return P();
        P ret(*this);
        for(int i=0;i<(int)ret.size();i++){
            ret[i]*=i;
        }
        return ret>>1;
    }
    P integral(){
        P ret(*this);
        for(int i=0;i<(int)ret.size();i++){
            ret[i]/=i+1;
        }
        return ret<<1;
    }
    P log(int deg=-1){
        assert((*this)[0]==T(1));
        const int n=deg==-1?this->size():deg;
        return (diff()*inv(n)).pre(n-1).integral();
    }
    P exp(int deg=-1){
        assert((*this)[0]==T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=ret*(pre(i<<1)+1-ret.log(i<<1)).pre(i<<1);
        }
        return ret.pre(n);
    }
	P pow(int c,int deg=-1){
		// const int n=deg==-1?this->size():deg;
		// long long i=0;
		// P ret(*this);
		// while(i!=(int)this->size()&&ret[i]==0)i++;
		// if(i==(int)this->size())return P(n,0);
		// if(i*c>=n)return P(n,0);
		// T k=ret[i];
		// return ((((ret>>i)/k).log()*c).exp()*(k.pow(c))<<(i*c)).pre(n);
        P x(*this);
        P ret(1,1);
        while(c) {
            if(c&1){
                ret*=x;
                if(~deg)ret=ret.pre(deg);
            }
            x*=x;
            if(~deg)x=x.pre(deg);
            c>>=1;
        }
        return ret;
	}
    P sqrt(int deg=-1){
        const int n=deg==-1?this->size():deg;
        if((*this)[0]==T(0)) {
            for(int i=1;i<(int)this->size();i++) {
                if((*this)[i]!=T(0)) {
                    if(i&1)return{};
                    if(n-i/2<=0)break;
                    auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
                    if((int)ret.size()<n)ret.resize(n,T(0));
                    return ret;
                }
            }
            return P(n,0);
        }
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=(ret+pre(i<<1)*ret.inv(i<<1)).pre(i<<1)/T(2);
        }
        return ret.pre(n);
    }
	P shift(int c){
		const int n=this->size();
		P f(*this),g(n,0);
		for(int i=0;i<n;++i)f[i]*=T(i).fact();
		for(int i=0;i<n;++i)g[i]=T(c).pow(i)/T(i).fact();
		g=g.rev();
		f*=g;
		f>>=n-1;
		for(int i=0;i<n;++i)f[i]/=T(i).fact();
		return f;
	}
    T eval(T x){
        T res=0;
        for(int i=(int)this->size()-1;i>=0;--i){
            res*=x;
            res+=(*this)[i];
        }
        return res;
    }
    vector<T> multipoint_eval(const vector<T>&x){
        const int n=x.size();
        P* v=new P[2*n-1];
        for(int i=0;i<n;i++)v[i+n-1]={T()-x[i],T(1)};
        for(int i=n-2;i>=0;i--){v[i]=v[i*2+1]*v[i*2+2];}
        v[0]=P(*this)%v[0];v[0].shrink();
        for(int i=1;i<n*2-1;i++){
            v[i]=v[(i-1)/2]%v[i];
            v[i].shrink();
        }
        vector<T>res(n);
        for(int i=0;i<n;i++)res[i]=v[i+n-1][0];
        return res;
    }
    P slice(int s,int e,int k){
        P res;
        for(int i=s;i<e;i+=k)res.push_back((*this)[i]);
        return res;
    }
    T nth_term(P q,int64_t x){
        if(x==0)return (*this)[0]/q[0];
        P p(*this);
        P q2=q;
        for(int i=1;i<(int)q2.size();i+=2)q2[i]*=-1;
        q*=q2;
        p*=q2;
        return p.slice(x%2,p.size(),2).nth_term(q.slice(0,q.size(),2),x/2);
    }
    
    //(*this)(t(x))
    P manipulate(P t,int deg){
        P s=P(*this);
        if(deg==0)return P();
        if((int)t.size()==1)return P{s.eval(t[0])};
        int k=min((int)std::sqrt(deg/(std::log2(deg)+1))+1,(int)t.size());
        int b=deg/k+1;
        P t2=t.pre(k);
        vector<P>table(s.size()/2+1,P{1});
        for(int i=1;i<(int)table.size();i++){
            table[i]=((table[i-1])*t2).pre(deg);
        }
        auto f=[&](auto f,auto l,auto r,int deg)->P{
            if(r-l==1)return P{*l};
            auto m=l+(r-l)/2;
            return f(f,l,m,deg)+(table[m-l]*f(f,m,r,deg)).pre(deg);
        };
        P ans=P();
        P tmp=f(f,s.begin(),s.end(),deg);
        P tmp2=P{1};
        T tmp3=T(1);
        P tmp4=t2.diff().inv(deg);
        for(int i=0;i<b;++i){
            ans+=(tmp*tmp2).pre(deg)/tmp3;
            tmp=(tmp.diff()*tmp4).pre(deg);
            tmp2=(tmp2*(t-t2)).pre(deg);
            tmp3*=T(i+1);
        }
        return ans;
    }
    //(*this)(t(x))
    P manipulate2(P t,int deg){
        P ans=P();
        P s=(*this).rev();
        for(int i=0;i<(int)s.size();++i){
            ans=(ans*t+s[i]).pre(deg);
        }
        return ans;
    }
};

template<typename Mint>
struct _FPS_FFT_MOD{
    template<typename P>
    P operator()(P s,P t){
        vector<double> s1(s.size()),s2(s.size());
        vector<double> t1(t.size()),t2(t.size());
        vector<double> u1(s.size()),u2(t.size());
        for(int i=0;i<(int)s.size();++i){
            s1[i]=s[i].value()&((1<<15)-1);
            s2[i]=s[i].value()>>15;
            u1[i]=s1[i]+s2[i];
        }
        for(int i=0;i<(int)t.size();++i){
            t1[i]=t[i].value()&((1<<15)-1);
            t2[i]=t[i].value()>>15;
            u2[i]=t1[i]+t2[i];
        }
        vector<double> a=mul(s1,t1);
        vector<double> c=mul(s2,t2);
        vector<double> b=mul(u1,u2);
        const int n=s.size()+t.size()-1;
        P res(n);
        Mint x=Mint(2).pow(15);
        for(int i=0;i<n;++i){
            res[i]=(Mint(round(c[i]))*x+Mint(round(b[i])-round(a[i])-round(c[i])))*x+Mint(round(a[i]));
        }
        return res;
    }
    vector<double> mul(vector<double> s,vector<double> t){
        const int n=s.size()+t.size()-1;
        int sz=1;
        while(sz<n)sz<<=1;
        complex<double>* a=new complex<double>[sz]();
        complex<double>* b=new complex<double>[sz];
        decltype(s) res(n);
        for(int i=0;i<(int)s.size();i++)a[i].real(s[i]);
        for(int i=0;i<(int)t.size();i++)a[i].imag(t[i]);
        fft(sz,a);
        for(int i=0;i<sz;i++){
            int j=i==0?0:sz-i;
            b[i]=(a[i]+conj(a[j]))*(a[i]-conj(a[j]))*complex<double>(0,-.25);
        }
        ifft(sz,b);
        for(int i=0;i<n;i++){
            res[i]=b[i].real();
        }
        return res;
    }
    struct complex_t { double Re, Im; };
    __m256d mulpz2(const __m256d ab, const __m256d xy){
        const __m256d aa = _mm256_unpacklo_pd(ab, ab);
        const __m256d bb = _mm256_unpackhi_pd(ab, ab);
        const __m256d yx = _mm256_shuffle_pd(xy, xy, 5);
        return _mm256_addsub_pd(_mm256_mul_pd(aa, xy), _mm256_mul_pd(bb, yx));
    }

    void fft0(int n, int s, bool eo, complex_t* x, complex_t* y){
        const int m = n/2;
        const double theta0 = 2*M_PI/n;

        if (n == 2) {
            complex_t* z = eo ? y : x;
            if (s == 1) {
                double* xd = &x->Re;
                double* zd = &z->Re;
                const __m128d a = _mm_load_pd(xd + 2*0);
                const __m128d b = _mm_load_pd(xd + 2*1);
                _mm_store_pd(zd + 2*0, _mm_add_pd(a, b));
                _mm_store_pd(zd + 2*1, _mm_sub_pd(a, b));
            }
            else {
                for (int q = 0; q < s; q += 2) {
                    double* xd = &(x + q)->Re;
                    double* zd = &(z + q)->Re;
                    const __m256d a = _mm256_load_pd(xd + 2*0);
                    const __m256d b = _mm256_load_pd(xd + 2*s);
                    _mm256_store_pd(zd + 2*0, _mm256_add_pd(a, b));
                    _mm256_store_pd(zd + 2*s, _mm256_sub_pd(a, b));
                }
            }
        }
        else if (n >= 4) {
            if (s == 1) {
                for (int p = 0; p < m; p += 2) {
                    const double cs0 = cos((p+0)*theta0);
                    const double sn0 = sin((p+0)*theta0);
                    const double cs1 = cos((p+1)*theta0);
                    const double sn1 = sin((p+1)*theta0);
                    const __m256d wp = _mm256_setr_pd(cs0, -sn0, cs1, -sn1);
                    double* xd = &(x + p)->Re;
                    double* yd = &(y + 2*p)->Re;
                    const __m256d a = _mm256_load_pd(xd + 2*0);
                    const __m256d b = _mm256_load_pd(xd + 2*m);
                    const __m256d aA =            _mm256_add_pd(a, b);
                    const __m256d bB = mulpz2(wp, _mm256_sub_pd(a, b));
                    const __m256d ab = _mm256_permute2f128_pd(aA, bB, 0x20);
                    const __m256d AB = _mm256_permute2f128_pd(aA, bB, 0x31);
                    _mm256_store_pd(yd + 2*0, ab);
                    _mm256_store_pd(yd + 2*2, AB);
                }
            }
            else {
                for (int p = 0; p < m; p++) {
                    const double cs = cos(p*theta0);
                    const double sn = sin(p*theta0);
                    const __m256d wp = _mm256_setr_pd(cs, -sn, cs, -sn);
                    for (int q = 0; q < s; q += 2) {
                        double* xd = &(x + q)->Re;
                        double* yd = &(y + q)->Re;
                        const __m256d a = _mm256_load_pd(xd + 2*s*(p + 0));
                        const __m256d b = _mm256_load_pd(xd + 2*s*(p + m));
                        _mm256_store_pd(yd + 2*s*(2*p + 0),            _mm256_add_pd(a, b));
                        _mm256_store_pd(yd + 2*s*(2*p + 1), mulpz2(wp, _mm256_sub_pd(a, b)));
                    }
                }
            }
            fft0(n/2, 2*s, !eo, y, x);
        }
    }
    void fft(int N, std::complex<double>* x){
        complex_t* y = (complex_t*) _mm_malloc(N*sizeof(complex_t), 32);
        complex_t* z = (complex_t*) _mm_malloc(N*sizeof(complex_t), 32);
        for (int p = 0; p < N; p++) {
            y[p].Re = x[p].real();
            y[p].Im = x[p].imag();
        }
        fft0(N, 1, 0, y, z);
        for(int k = 0; k < N; k++)x[k] = std::complex<double>(y[k].Re, y[k].Im);
        _mm_free(z);
        _mm_free(y);
    }

    void ifft(int N, std::complex<double>* x){
        complex_t* y = (complex_t*) _mm_malloc(N*sizeof(complex_t), 32);
        complex_t* z = (complex_t*) _mm_malloc(N*sizeof(complex_t), 32);
        for (int p = 0; p < N; p++) {
            y[p].Re =  x[p].real();
            y[p].Im = -x[p].imag();
        }
        fft0(N, 1, 0, y, z);
        for (int k = 0; k < N; k++)x[k] = std::complex<double>(y[k].Re/N, -y[k].Im/N);
        _mm_free(z);
        _mm_free(y);
    }
};
template<typename Mint>using fps=FPS_BASE<Mint,_FPS_FFT_MOD<Mint>>;

class mint {
  using u64 = std::uint_fast64_t;
    public:
    u64 a;
    constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
    constexpr u64 &value()noexcept{return a;}
    constexpr const u64 &value() const noexcept {return a;}
    constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
    constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
    constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
    constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
    constexpr mint &operator+=(const mint rhs) noexcept {
        a += rhs.a;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint &operator-=(const mint rhs) noexcept {
        if (a<rhs.a)a += get_mod();
        a -= rhs.a;
        return *this;
    }
    constexpr mint &operator*=(const mint rhs) noexcept {
        a = a * rhs.a % get_mod();
        return *this;
    }
    constexpr mint operator++(int) noexcept {
        a += 1;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint operator--(int) noexcept {
        if (a<1)a += get_mod();
        a -= 1;
        return *this;
    }
    constexpr mint &operator/=(mint rhs) noexcept {
        u64 exp=get_mod()-2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    constexpr bool operator==(mint x) noexcept {
        return a==x.a;
    }
    constexpr bool operator!=(mint x) noexcept {
        return a!=x.a;
    }
    constexpr bool operator<(mint x) noexcept {
        return a<x.a;
    }
    constexpr bool operator>(mint x) noexcept {
        return a>x.a;
    }
    constexpr bool operator<=(mint x) noexcept {
        return a<=x.a;
    }
    constexpr bool operator>=(mint x) noexcept {
        return a>=x.a;
    }
    constexpr static int root(){
        mint root = 2;
        while(root.pow((get_mod()-1)>>1).a==1)root++;
        return root.a;
    }
    constexpr mint pow(long long n){
        long long x=a;
        mint ret = 1;
        while(n>0) {
            if(n&1)(ret*=x);
            (x*=x)%=get_mod();
            n>>=1;
        }
        return ret;
    }
    constexpr mint inv(){
        return pow(get_mod()-2);
    }
    static vector<mint> fac,ifac;
    static bool init;
    constexpr static int mx=10000001;
    void build(){
        init=0;
        fac.resize(mx);
        ifac.resize(mx);
        fac[0]=1,ifac[0]=1;
        for(int i=1;i<mx;i++)fac[i]=fac[i-1]*i;
        ifac[mx-1]=fac[mx-1].inv();
        for(int i=mx-2;i>=0;i--)ifac[i]=ifac[i+1]*(i+1);
    }
    mint comb(long long b){
        if(init)build();
        if(a==0&&b==0)return 1;
        if((long long)a<b)return 0;
        return fac[a]*ifac[a-b]*ifac[b];
    }
    mint fact(){
        if(init)build();
        return fac[a];
    }
    mint fact_inv(){
        if(init)build();
        return ifac[a];
    }
    friend ostream& operator<<(ostream& lhs, const mint& rhs) noexcept {
        lhs << rhs.a;
        return lhs;
    }
    friend istream& operator>>(istream& lhs,mint& rhs) noexcept {
        lhs >> rhs.a;
        return lhs;
    }
    constexpr static u64 get_mod(){return MOD;}
};
vector<mint> mint::fac;
vector<mint> mint::ifac;
bool mint::init=1;

int main(){
    lint n,k;
    cin>>n>>k;
    vec a(k);
    rep(i,k)cin>>a[i];
    fps<mint>f{1};
    rep(i,k){
        fps<mint>g(a[i]+1);
        rep(j,a[i]+1){
            g[j]=mint(n-j).comb(a[i]-j)/mint(j).fact();
        }
        f*=g;
        f=f.pre(n+1);
    }
    f.resize(n+1,0);
    cout<<f[n]*mint(n).fact()<<endl;
}

Measured memory_bytes: 164028