#include<bits/stdc++.h>
using namespace std;
#define int long long


typedef long long ll;
const int p=998244353;
int po(int a,int b) {if(b==0) return 1; if(b==1) return a; if(b%2==0) {int u=po(a,b/2);return (u*1LL*u)%p;} else {int u=po(a,b-1);return (a*1LL*u)%p;}}
int inv(int x) {return po(x,p-2);}
template<int M, int K, int G> struct Fft {
    // 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...
    int g[1 << (K - 1)];
    Fft() : g() { //if tl constexpr...
        static_assert(K >= 2, "Fft: K >= 2 must hold");
        g[0] = 1;
        g[1 << (K - 2)] = G;
        for (int l = 1 << (K - 2); l >= 2; l >>= 1) {
            g[l >> 1] = (static_cast<long long>(g[l]) * g[l]) % M;
        }
        assert((static_cast<long long>(g[1]) * g[1]) % M == M - 1);
        for (int l = 2; l <= 1 << (K - 2); l <<= 1) {
            for (int i = 1; i < l; ++i) {
                g[l + i] = (static_cast<long long>(g[l]) * g[i]) % M;
            }
        }
    }
    void fft(vector<int> &x) const {
        const int n = x.size();
        assert(!(n & (n - 1)) && n <= 1 << K);
        for (int h = __builtin_ctz(n); h--; ) {
            const int l = 1 << h;
            for (int i = 0; i < n >> 1 >> h; ++i) {
                for (int j = i << 1 << h; j < ((i << 1) + 1) << h; ++j) {
                    const int t = (static_cast<long long>(g[i]) * x[j | l]) % M;
                    if ((x[j | l] = x[j] - t) < 0) x[j | l] += M;
                    if ((x[j] += t) >= M) x[j] -= M;
                }
            }
        }
        for (int i = 0, j = 0; i < n; ++i) {
            if (i < j) std::swap(x[i], x[j]);
            for (int l = n; (l >>= 1) && !((j ^= l) & l); ) {}
        }
    }
    vector<int> convolution(const vector<int> &a, const vector<int> &b) const {
        if(a.empty() || b.empty()) return {};
        const int na = a.size(), nb = b.size();
        int n, invN = 1;
        for (n = 1; n < na + nb - 1; n <<= 1) invN = ((invN & 1) ? (invN + M) : invN) >> 1;
        vector<int> x(n, 0), y(n, 0);
        std::copy(a.begin(), a.end(), x.begin());
        std::copy(b.begin(), b.end(), y.begin());
        fft(x);
        fft(y);
        for (int i = 0; i < n; ++i) x[i] = (((static_cast<long long>(x[i]) * y[i]) % M) * invN) % M;
        std::reverse(x.begin() + 1, x.end());
        fft(x);
        x.resize(na + nb - 1);
        return x;
    }
};
Fft<998244353,23,31> muls;
vector<int> form(vector<int> v,int n)
{
    while(v.size()<n) v.push_back(0);
    while(v.size()>n) v.pop_back();
    return v;
}
vector<int> operator *(vector<int> v1,vector<int> v2)
{
    return muls.convolution(v1,v2);
}
vector<int> operator +(vector<int> v1,vector<int> v2)
{
    while(v2.size()<v1.size()) v2.push_back(0); while(v1.size()<v2.size()) v1.push_back(0);
    for(int i=0;i<v1.size();++i) {v1[i]+=v2[i];if(v1[i]>=p) v1[i]-=p; else if(v1[i]<0) v1[i]+=p;}
    return v1;
}
vector<int> operator -(vector<int> v1,vector<int> v2)
{
    int sz=max(v1.size(),v2.size());while(v1.size()<sz) v1.push_back(0); while(v2.size()<sz) v2.push_back(0);
    for(int i=0;i<sz;++i) {v1[i]-=v2[i];if(v1[i]<0) v1[i]+=p; else if(v1[i]>=p) v1[i]-=p;} return v1;
}
vector<int> trmi(vector<int> v)
{
    for(int i=1;i<v.size();i+=2) {if(v[i]>0) v[i]=p-v[i]; else v[i]=(-v[i]);}
    return v;
}
vector<int> deriv(vector<int> v)
{
    if(v.empty()) return{};
    vector<int> ans(v.size()-1);
    for(int i=1;i<v.size();++i) ans[i-1]=(v[i]*1LL*i)%p;
    return ans;
}
vector<int> integ(vector<int> v)
{
    vector<int> ans(v.size()+1);ans[0]=0;
    for(int i=1;i<v.size();++i) ans[i-1]=(v[i]*1LL*i)%p;
    return ans;
}
vector<int> mul(vector<vector<int> > v)
{
    if(v.size()==1) return v[0];
    vector<vector<int> > v1,v2;for(int i=0;i<v.size()/2;++i) v1.push_back(v[i]); for(int i=v.size()/2;i<v.size();++i) v2.push_back(v[i]);
    return muls.convolution(mul(v1),mul(v2));
}
vector<int> inv1(vector<int> v,int n)
{
    assert(v[0]!=0);
    int sz=1;v=form(v,n);vector<int> a={inv(v[0])};
    while(sz<n)
    {
        vector<int> vsz;for(int i=0;i<min(n,2*sz);++i) vsz.push_back(v[i]);
        vector<int> b=((vector<int>) {1})-muls.convolution(a,vsz);
        for(int i=0;i<sz;++i) assert(b[i]==0);
        b.erase(b.begin(),b.begin()+sz);
        vector<int> c=muls.convolution(b,a);
        for(int i=0;i<sz;++i) a.push_back(c[i]);
        sz*=2;
    }
    return form(a,n);
}

vector<int> inv(vector<int> v,int n)
{
    v=form(v,n);assert(v[0]!=0);if(v.size()==1) {return {inv(v[0])};} vector<int> v1=trmi(v);
    vector<int> a=v1*v;a=form(a,2*n);
    vector<int> b((n+1)/2);for(int i=0;i<b.size();++i) b[i]=a[2*i];
    vector<int> ans1=inv(b,b.size());vector<int> ans2(n);for(int i=0;i<n;++i) {if(i%2==0) ans2[i]=ans1[i/2]; else ans2[i]=0;}
    return form(v1*ans2,n);
}
vector<int> operator/(vector<int> a,vector<int> b)
{
    while(!a.empty() && a.back()==0) a.pop_back(); while(!b.empty() && b.back()==0) b.pop_back();
    int n=a.size();int m=b.size();if(n<m) return {};
    reverse(a.begin(),a.end());reverse(b.begin(),b.end());vector<int> ans=a*inv(b,n-m+1);while(ans.size()>n-m+1) ans.pop_back();
    reverse(ans.begin(),ans.end());while(!ans.empty() && ans.back()==0) ans.pop_back();return ans;
}
vector<int> operator%(vector<int> a,vector <int> b)
{
    vector<int> ans=a-b*(a/b);while(!ans.empty() && ans.back()==0) ans.pop_back(); return ans;
}
const int md = p;

const int N=12;
int sa[1<<N],sb[1<<N];
int Bit(int mask, int i) {
    return (mask >> i)&1;
}
vector <int> o[12],u[1<<12];
int pr[1<<12][12][1005];
int C[1005][1005],invC[1005][1005];
int dp[1<<12][1005];
int zx[1<<12][1005];
int izx[1<<12][1005];
int32_t main() {
#ifdef LOCAL
    freopen("../A.in", "r", stdin);
#endif
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    for (int i = 0; i < 1005; ++i) {C[i][0]=1;}
    for (int i = 1; i < 1005; ++i) {
        for (int j = 1; j < 1005; ++j) {
            C[i][j] = (C[i - 1][j] + C[i - 1][j - 1])%md;
        }
    }
   for(int i=0;i<1005;++i) for(int j=0;j<=i;++j) invC[i][j] = po(C[i][j],md-2);
    int invm[1005];
    for(int i=0;i<1005;++i) invm[i]=po(i,md-2);
    int n, m;
    cin >> m>>n;
    vector <int> a(n), b(n);
    for (int i = 0;i<n;++i){cin>>a[i];}
    for (int i = 0;i<n;++i){cin>>b[i];}
    for (int mask = 1;mask<(1<<n);++mask){
        for ( int i = 0;i<n;++i){
            if(Bit(mask,i)){
                sa[mask]=sa[mask^(1<<i)]+a[i];
                sb[mask]=sb[mask^(1<<i)]+b[i];
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < b[i]; ++j) {
            o[i].push_back(C[a[i]][j]);
        }
    }
    u[0]={1};
    for (int mask = 1; mask < (1 << n); ++mask) {
        for (int i = 0; i < n; ++i) {
            if (Bit(mask, i)) {
                u[mask] = u[mask^(1<<i)]*o[i];
                break;
            }
        }
    }
    auto cf = [&] (vector <int> &a, int i) {
        if (i < (int)a.size()) {
            return a[i];
        }
        else {
            return 0ll;
        }
    };
    for (int mask = 0; mask < (1 << n); ++mask) {
        bool ok = 1;

        for (int i = 0; i < n; ++i) {
            if (Bit(mask, i)) ok &= !!b[i];
        }

        if (ok) {
            for (int i = 0; i < n; ++i) {
                if (Bit(mask, i)) {
                    for (int m = b[i]; m <= sb[mask]; ++m) {
                        int x = cf(u[mask-(1<<i)],m-b[i]);
                        x *= C[a[i]][b[i]-1];
                        x %= md;
                        x *= invC[sa[mask]][m-1];x%=md;
                        x*=(a[i]-b[i]+1);x%=md;
                        x*=invm[sa[mask]-m+1];x%=md;
                        pr[mask][i][m]=x;
                    }
                }

            }
        }
        else {

        }
    }
    for(int mask=0;mask<(1<<n);++mask)
    {
        for(int i=1002;i>=0;--i)
        {
            zx[mask][i]=zx[mask][i+1];
            for(int j=0;j<n;++j)
            {
                if(mask & (1<<j))
                {
                    zx[mask][i]+=pr[mask][j][i];zx[mask][i]%=md;
                }
            }
            izx[mask][i]=po(zx[mask][i],md-2);
        }
    }
    for (int mask = 1; mask < (1 << n); ++mask) {
        bool ok = 1;
        for (int i = 0; i < n; ++i) {
            if (Bit(mask, i)) ok &= !!b[i];
        }
        if(!ok){continue;}
        for (int m=sb[mask];m>=0;--m){
            int sp = 0;
            for (int i = 0; i < n; ++i) {
                if (!Bit(mask,i)) continue;
                int p2=pr[mask][i][m+1]*izx[mask][m+1];p2%=md;
                sp += p2;sp%=md;
                dp[mask][m]+=dp[mask-(1<<i)][m+1-b[i]]*p2;
                dp[mask][m]%=md;
            }
            sp %= md;
            dp[mask][m]+=dp[mask][m+1]*(md+1-sp);dp[mask][m]%=md;dp[mask][m]%=md;
            dp[mask][m]+=(sa[mask]-m+sa[(1<<n)-mask-1]-sb[(1<<n)-mask-1])*invm[sa[mask]-m];
            dp[mask][m]%=md;
        }

    }
    int ma = 0;
    for (int i = 0; i < n; ++i) {
        if (b[i]) {
            ma += 1 << i;
        }
    }
    cout << ((dp[ma][0]%p)+p)%p;
    return 0;
}