#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(int)a;i<(int)b;i++)
using ll =long long;
#define all(p) p.begin(),p.end()
const int mod=998244353;
struct mint {
    static constexpr int m=998244353;
    int x;
    mint():x(0){}
    mint(ll x_):x(x_%m){if(x<0)x+=m;}
    mint &operator+=(mint b){if((x+=b.x)>=m)x-=m;return *this;}
    mint &operator-=(mint b){if((x-=b.x)<0) x+=m;return *this;}
    mint &operator*=(mint b){x=(ll)(x)*b.x%m;return *this;}
    mint pow(ll e)const{
        mint r=1,b=*this;
        while(e){
            if(e&1) r*=b;
            b*=b;
            e>>=1;
        }
        return r;
    }
    mint inv(){return pow(m-2);}
    mint operator/=(mint b){return *this*=b.inv();}
    friend mint operator+(mint a,mint b){return a+=b;}
    friend mint operator-(mint a,mint b){return a-=b;}
    friend mint operator*(mint a,mint b){return a*=b;}
    friend mint operator/(mint a,mint b){return a/=b;}
};

mint G=3;
void ntt(bool inv,vector<mint> &a){
    int n=a.size(),s=__lg(n);
    assert(1<<s==n);
    static vector<mint> ep,iep;
    while(ep.size()<=s){
        ep.push_back(G.pow((mod-1)>>ep.size()));
        iep.push_back(ep.back().inv());
    }
    vector<mint> b(n);
    rep(i,1,s+1){
        int w=1<<(s-i);
        mint base=inv?iep[i]:ep[i],now=1;
        for(int y=0;y<n/2;y+=w){
            rep(x,0,w){
                auto l=a[y<<1|x];
                auto r=now*a[y<<1|x|w];
                b[y|x]=l+r;
                b[y|x|n>>1]=l-r;
            }
            now*=base;
        }
        swap(a,b);
    }
}
vector<mint> mult(const vector<mint> &a,const vector<mint> &b){
    const int n=a.size(),m=b.size();
    if(!n||!m) return {};
    int z=1;
    while(z<n+m-1) z<<=1;
    auto a2=a,b2=b;
    a2.resize(z),b2.resize(z);
    ntt(0,a2),ntt(0,b2);
    rep(i,0,z) a2[i]*=b2[i];
    ntt(1,a2);
    a2.resize(n+m-1);
    mint iz=mint(z).inv();
    rep(i,0,n+m-1) a2[i]*=iz;
    return a2;
}

const int len=1100;
vector<mint> fact(len,1);
vector<mint> fact_rev(len,1);

void fact_init(){
    rep(i,1,len) fact[i]=fact[i-1]*i;
    fact_rev[len-1]=fact[len-1].inv();
    for(int i=len-1;i>0;i--) fact_rev[i-1]=fact_rev[i]*i;
}

mint comb(int a,int b){
    if(a<b||b<0) return 0;
    return fact[a]*fact_rev[a-b]*fact_rev[b];
}

mint rev(int a){
    if(0<a&&a<len) return fact[a-1]*fact_rev[a];
    return ((mint)(a)).inv();
}

void solve(){
    fact_init();
    int N,M;
    cin>>N>>M;
    vector<int> A(M),B(M);
    rep(i,0,M) cin>>A[i];
    rep(i,0,M) cin>>B[i];
    int L=N+5;
    vector<vector<mint>> f(M),g(M);
    rep(i,0,M){
        g[i].resize(L*(A[i]-B[i]+1),0);
        rep(j,B[i],A[i]+1){
            g[i][j+L*(j-B[i])]=comb(A[i],j);
        }
        f[i]=g[i];
        rep(j,0,B[i]){
            f[i][j]=comb(A[i],j);
        }
    }
    rep(i,0,M-1) f.push_back(mult(f[i*2],f[i*2+1])),g.push_back(mult(g[i*2],g[i*2+1]));
    mint ans=0;
    rep(s,0,N) rep(t,0,N){
        if(s+t*L>=f[2*M-2].size()) break;
        auto tmp=f[2*M-2][s+t*L]-g[2*M-2][s+t*L];
        if(tmp.x==0) continue;
        ans+=tmp*fact[s]*fact[N-s]*(1+rev(N-s)*t);
    }
    ans*=fact_rev[N];
    cout<<(mod+ans.x%mod)%mod<<"\n";
}

/*
I

2 2
1 1
1 1

2
---
4 2
2 2
2 1

582309210
---
1000 12
101 43 34 281 23 24 12 25 66 222 145 24
37 43 27 257 5 11 12 19 62 41 87 13

265294941
 */
int main(){
    int t=1;//cin>>t;
    rep(i,0,t) solve();
}