#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto& i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}
#define retval(x) {cout << #x << endl; return;}
#define cout2(x,y) cout << x << " " << y << endl;
#define coutp(p) cout << p.fi << " " << p.se << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define assertmle(x) if (!(x)) {vi v(3e8);}
#define asserttle(x) if (!(x)) {while(1){}}
#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define coutv2(v) fore(vy , v) cout << vy << "\n";
#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = dynamic_modint<0>;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define no {cout <<"No"<<endl;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#ifdef MY_LOCAL_DEBUG
#include "./debug/localDebug.cpp"
#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl
#define show1(a) cerr<<#a<<" = "<<a<<endl
#define show2(a,b) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<endl
#define show3(a,b,c) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<endl
#define show4(a,b,c,d) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<endl
#define show5(a,b,c,d,e) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<" : "<<#e<<" = "<<e<<endl
#define DEBUG_LINE cout << "DEBUG_LINE : " << __LINE__ << endl
#define showv(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) {cout<<#v<<endl; fore(vy , v) cout << vy << "\n";}
#define showvm(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) {cout<<#v<<endl; fore(vy , v) cout << vy.val() << "\n";}
#define showmat(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg << " "; cout << endl;}}
#define showmatm(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg.val() << " "; cout << endl;}}
#else
#define showp(p)
#define show1(a)
#define show2(a,b)
#define show3(a,b,c)
#define show4(a,b,c,d)
#define show5(a,b,c,d,e)
#define DEBUG_LINE
#define showv(v)
#define showv2(v)
#define showvm(v)
#define showvm2(v)
#define showmat(v)
#define showmatm(v)
#endif
#define overload5(a,b,c,d,e,f, ...) f
#define show(...) overload5(__VA_ARGS__, show5, show4, show3, show2, show1)(__VA_ARGS__)

struct NTT
{
    uint32_t get_pr()
    {
        uint32_t _mod = mint::mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for (u64 i = 2; i * i <= m; ++i)
        {
            if (m % i == 0)
            {
                ds[idx++] = i;
                while (m % i == 0)
                    m /= i;
            }
        }
        if (m != 1)
            ds[idx++] = m;
    
        uint32_t _pr = 2;
        while (1)
        {
            int flg = 1;
            for (int i = 0; i < idx; ++i)
            {
                u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
                while (b)
                {
                    if (b & 1)
                        r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if (r == 1)
                {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1)
                break;
            ++_pr;
        }
        return _pr;
    };
    static constexpr uint32_t mod = mint::mod();
    uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];
    void setwy(int k)
    {
        mint w[level], y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inv();
        for (int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for (int i = 3; i < k; ++i)
        {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }
    NTT() { setwy(level); }
    void fft4(vector<mint> &a, int k)
    {
        if ((int)a.size() <= 1)
            return;
        if (k == 1)
        {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1)
        {
            int v = 1 << (k - 1);
            for (int j = 0; j < v; ++j)
            {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v)
        {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3)
                {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dw[2], wx = one;
            for (int jh = 4; jh < u;)
            {
                ww = xx * xx, wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2)
                {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
                         t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }
    void ifft4(vector<mint> &a, int k)
    {
        if ((int)a.size() <= 1)
            return;
        if (k == 1)
        {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u)
        {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = v + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3)
                {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dy[2], yy = one;
            u <<= 2;
            for (int jh = 4; jh < u;)
            {
                ww = xx * xx, yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2)
                {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1)
        {
            u = 1 << (k - 1);
            for (int j = 0; j < u; ++j)
            {
                mint ajv = a[j] - a[j + u];
                a[j] += a[j + u];
                a[j + u] = ajv;
            }
        }
    }
    void ntt(vector<mint> &a)
    {
        if ((int)a.size() <= 1)
            return;
        fft4(a, __builtin_ctz(a.size()));
    }
    void intt(vector<mint> &a)
    {
        if ((int)a.size() <= 1)
            return;
        ifft4(a, __builtin_ctz(a.size()));
        mint iv = mint(a.size()).inv();
        for (auto &x : a)
            x *= iv;
    }
    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b)
    {
        int l = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40)
        {
            vector<mint> s(l);
            for (int i = 0; i < (int)a.size(); ++i)
                for (int j = 0; j < (int)b.size(); ++j)
                    s[i + j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < l)
            M <<= 1, ++k;
        setwy(k);
        vector<mint> s(M), t(M);
        for (int i = 0; i < (int)a.size(); ++i)
            s[i] = a[i];
        for (int i = 0; i < (int)b.size(); ++i)
            t[i] = b[i];
        fft4(s, k);
        fft4(t, k);
        for (int i = 0; i < M; ++i)
            s[i] *= t[i];
        ifft4(s, k);
        s.resize(l);
        mint invm = mint(M).inv();
        for (int i = 0; i < l; ++i)
            s[i] *= invm;
        return s;
    }
    void ntt_doubling(vector<mint> &a)
    {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++)
            b[i] *= r, r *= zeta;
        ntt(b);
        copy(begin(b), end(b), back_inserter(a));
    }
};

struct FPS : vector<mint>
{
    using vector<mint>::vector;
    FPS &operator+=(const FPS &r)
    {
        if (r.size() > this->size())
            this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++)
            (*this)[i] += r[i];
        return *this;
    }
    FPS &operator+=(const mint &r)
    {
        if (this->empty())
            this->resize(1);
        (*this)[0] += r;
        return *this;
    }
    FPS &operator-=(const FPS &r)
    {
        if (r.size() > this->size())
            this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++)
            (*this)[i] -= r[i];
        return *this;
    }
    FPS &operator-=(const mint &r)
    {
        if (this->empty())
            this->resize(1);
        (*this)[0] -= r;
        return *this;
    }
    FPS &operator*=(const mint &v)
    {
        for (int k = 0; k < (int)this->size(); k++)
            (*this)[k] *= v;
        return *this;
    }
    FPS &operator/=(const FPS &r)
    {
        if (this->size() < r.size())
        {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        if ((int)r.size() <= 64)
        {
            FPS f(*this), g(r);
            g.shrink();
            mint coeff = g.back().inv();
            for (auto &x : g)
                x *= coeff;
            int deg = (int)f.size() - (int)g.size() + 1;
            int gs = g.size();
            FPS quo(deg);
            for (int i = deg - 1; i >= 0; i--)
            {
                quo[i] = f[i + gs - 1];
                for (int j = 0; j < gs; j++)
                    f[i + j] -= quo[i] * g[j];
            }
            *this = quo * coeff;
            this->resize(n, mint(0));
            return *this;
        }
        return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }
    FPS &operator%=(const FPS &r)
    {
        *this -= *this / r * r;
        shrink();
        return *this;
    }
    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator+(const mint &v) const { return FPS(*this) += v; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator-(const mint &v) const { return FPS(*this) -= v; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator*(const mint &v) const { return FPS(*this) *= v; }
    FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
    FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
    FPS operator-() const
    {
        FPS ret(this->size());
        for (int i = 0; i < (int)this->size(); i++)
            ret[i] = -(*this)[i];
        return ret;
    }
    void shrink()
    {
        while (this->size() && this->back() == mint(0))
            this->pop_back();
    }
    FPS rev() const
    {
        FPS ret(*this);
        reverse(rng(ret));
        return ret;
    }
    FPS dot(FPS r) const
    {
        FPS ret(min(this->size(), r.size()));
        for (int i = 0; i < (int)ret.size(); i++)
            ret[i] = (*this)[i] * r[i];
        return ret;
    }
    FPS pre(int sz) const
    {
        return FPS((*this).begin(), (*this).begin() + min((int)this->size(), sz));
    }
    FPS operator>>(int sz) const
    {
        if ((int)this->size() <= sz)
            return {};
        FPS ret(*this);
        ret.erase(ret.begin(), ret.begin() + sz);
        return ret;
    }
    FPS operator<<(int sz) const
    {
        FPS ret(*this);
        ret.insert(ret.begin(), sz, mint(0));
        return ret;
    }
    FPS diff() const
    {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        mint one(1), coeff(1);
        for (int i = 1; i < n; i++)
        {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }
    FPS integral() const
    {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = mint(0);
        if (n > 0)
            ret[1] = mint(1);
        auto mod = mint::mod();
        for (int i = 2; i <= n; i++)
            ret[i] = (-ret[mod % i]) * (mod / i);
        for (int i = 0; i < n; i++)
            ret[i + 1] *= (*this)[i];
        return ret;
    }
    mint eval(mint x) const
    {
        mint r = 0, w = 1;
        for (auto &v : *this)
            r += w * v, w *= x;
        return r;
    }
    FPS log(int deg = -1) const
    {
        assert((*this)[0] == mint(1));
        if (deg == -1)
            deg = (int)this->size();
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }
    FPS pow(int64_t k, int deg = -1) const
    {
        const int n = (int)this->size();
        if (deg == -1)
            deg = n;
        if (k == 0)
        {
            FPS ret(deg);
            if (deg)
                ret[0] = 1;
            return ret;
        }
        for (int i = 0; i < n; i++)
        {
            if ((*this)[i] != mint(0))
            {
                mint rev = mint(1) / (*this)[i];
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
                ret *= (*this)[i].pow(k);
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg)
                    ret.resize(deg, mint(0));
                return ret;
            }
            if (__int128_t(i + 1) * k >= deg)
                return FPS(deg, mint(0));
        }
        return FPS(deg, mint(0));
    }
    static void *ntt_ptr;
    void set_fft()
    {
        if (!ntt_ptr)
            ntt_ptr = new NTT;
    }
    FPS &operator*=(
        const FPS &r)
    {
        if (this->empty() || r.empty())
        {
            this->clear();
            return *this;
        }
        set_fft();
        auto ret = static_cast<NTT *>(ntt_ptr)->multiply(*this, r);
        return *this = FPS(ret.begin(), ret.end());
    }
    void ntt()
    {
        set_fft();
        static_cast<NTT *>(ntt_ptr)->ntt(*this);
    }
    void intt()
    {
        set_fft();
        static_cast<NTT *>(ntt_ptr)->intt(*this);
    }
    void ntt_doubling()
    {
        set_fft();
        static_cast<NTT *>(ntt_ptr)->ntt_doubling(*this);
    }
    int ntt_pr()
    {
        set_fft();
        return static_cast<NTT *>(ntt_ptr)->pr;
    }
    FPS inv(int deg) const
    {
        assert((*this)[0] != mint(0));
        if (deg == -1)
            deg = (int)this->size();
        FPS res(deg);
        res[0] = {mint(1) / (*this)[0]};
        for (int d = 1; d < deg; d <<= 1)
        {
            FPS f(2 * d), g(2 * d);
            for (int j = 0; j < min((int)this->size(), 2 * d); j++)
                f[j] = (*this)[j];
            for (int j = 0; j < d; j++)
                g[j] = res[j];
            f.ntt();
            g.ntt();
            for (int j = 0; j < 2 * d; j++)
                f[j] *= g[j];
            f.intt();
            for (int j = 0; j < d; j++)
                f[j] = 0;
            f.ntt();
            for (int j = 0; j < 2 * d; j++)
                f[j] *= g[j];
            f.intt();
            for (int j = d; j < min(2 * d, deg); j++)
                res[j] = -f[j];
        }
        return res.pre(deg);
    }
    FPS exp(int deg) const
    {
        using fps = FPS;
        assert((*this).size() == 0 || (*this)[0] == mint(0));
        if (deg == -1)
            deg = this->size();
    
        fps inv;
        inv.reserve(deg + 1);
        inv.push_back(mint(0));
        inv.push_back(mint(1));
    
        auto inplace_integral = [&](fps &F) -> void
        {
            const int n = (int)F.size();
            auto mod = mint::mod();
            while ((int)inv.size() <= n)
            {
                int i = inv.size();
                inv.push_back((-inv[mod % i]) * (mod / i));
            }
            F.insert(F.begin(), mint(0));
            for (int i = 1; i <= n; i++)
                F[i] *= inv[i];
        };
        
        auto inplace_diff = [](fps &F) -> void
        {
            if (F.empty())
                return;
            F.erase(F.begin());
            mint coeff = 1, one = 1;
            for (int i = 0; i < (int)F.size(); i++)
            {
                F[i] *= coeff;
                coeff += one;
            }
        };
        
        fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
        for (int m = 2; m < deg; m *= 2)
        {
            auto y = b;
            y.resize(2 * m);
            y.ntt();
            z1 = z2;
            fps z(m);
            for (int i = 0; i < m; ++i)
                z[i] = y[i] * z1[i];
            z.intt();
            fill(z.begin(), z.begin() + m / 2, mint(0));
            z.ntt();
            for (int i = 0; i < m; ++i)
                z[i] *= -z1[i];
            z.intt();
            c.insert(c.end(), z.begin() + m / 2, z.end());
            z2 = c;
            z2.resize(2 * m);
            z2.ntt();
            fps x((*this).begin(), (*this).begin() + min<int>(this->size(), m));
            x.resize(m);
            inplace_diff(x);
            x.push_back(mint(0));
            x.ntt();
            for (int i = 0; i < m; ++i)
                x[i] *= y[i];
            x.intt();
            x -= b.diff();
            x.resize(2 * m);
            for (int i = 0; i < m - 1; ++i)
                x[m + i] = x[i], x[i] = mint(0);
            x.ntt();
            for (int i = 0; i < 2 * m; ++i)
                x[i] *= z2[i];
            x.intt();
            x.pop_back();
            inplace_integral(x);
            for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
                x[i] += (*this)[i];
            fill(x.begin(), x.begin() + m, mint(0));
            x.ntt();
            for (int i = 0; i < 2 * m; ++i)
                x[i] *= y[i];
            x.intt();
            b.insert(b.end(), x.begin() + m, x.end());
        }
        return fps{b.begin(), b.begin() + deg};
    }
};
void *FPS::ntt_ptr = nullptr;

//FPSライブラリ
//除算 : f/g は右式のqを返す f = g*q + r
//pow(int64_t k, int deg = -1) : f^k mod x^deg

struct combination {
  vector<mint> fact, ifact;
  combination(int n):fact(n+1),ifact(n+1) {
    fact[0] = 1;
    for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fact[n]*ifact[k]*ifact[n-k];
  }
} com(10000005);

struct pack{
    int s;
    FPS f;

    pack(const FPS& f) : s(sz(f)), f(f) {}

    bool operator>(const pack& ot) const{
        return s > ot.s;
    }
};


void solve(){
    int n,m; cin>>n>>m;
    mpq<pack> v;
    v.push(pack(FPS(1,1)));
    rep(i,m){
        int l,r; cin>>l>>r;
        if ((r-l)%2==0) continue;
        int k = (r-l+1);
        FPS f(k+1);
        f[k] = - com(k, k/2) / (k/2+1);
        f[0] = 1;
        v.push(pack(f));
    }
    if (n%2==1) retval(0);

    while(sz(v) > 1){
        FPS f = v.top().f;
        v.pop();
        FPS g = v.top().f;
        v.pop();
        FPS nxt = f*g;
        v.push(pack(nxt));
    }
    FPS f = v.top().f;
    mint ans = 0;
    rep(i,sz(f)){
        int r = n-i;
        mint coef = com(r, r/2) / (r/2+1);
        ans += coef * f[i];
    }
    outm;

    return;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int t = 1;
    //cin>>t;

    rep(i,t){
        solve();
    }

    return 0;
}