#include <bits/stdc++.h>  // clang-format off
using namespace std;constexpr int INF=1001001001;constexpr long long INFll=1001001001001001001;namespace viewer{template <class T>string f(T i){string s=(i==INF||i==INFll?"inf":to_string(i));s=string(max(0,3-int(s.size())),' ')+s;return s;}
template<class T>auto v(T&x,string end)->decltype(cerr<<x){return cerr<<x<<end;}void v(int x,string end){cerr<<f(x)<<end;}void v(long long x,string end){cerr<<f(x)<<end;}void v(float x,string end){cerr<<fixed<<setprecision(16)<<x<<end;}void v(double x,string end){cerr<<fixed<<setprecision(16)<<x<<end;}void v(long double x,string end){cerr<<fixed<<setprecision(16)<<x<<end;}
template<class T,class U>void v(const pair<T,U>&p,string end="\n"){cerr<<"(";v(p.first,", ");v(p.second,")"+end);}template<class T,class U>void v(const tuple<T,U>&t,string end="\n"){auto[a,b]=t;cerr<<"(";v(a,", ");v(b,")"+end);}template<class T,class U,class V>void v(const tuple<T,U,V>&t,string end="\n"){auto[a,b,c]=t;cerr<<"(";v(a,", ");v(b,", ");v(c,")"+end);}template<class T,class U,class V,class W>void v(const tuple<T,U,V,W>&t,string end="\n"){auto[a,b,c,d]=t;cerr<<"(";v(a,", ");v(b,", ");v(c,", ");v(d,")"+end);}
template<class T>void v(const vector<T>&vx,string);template<class T>auto ve(int,const vector<T>&vx)->decltype(cerr<<vx[0]){cerr<<"{";for(const T&x:vx)v(x,",");return cerr<<"}\n";}template <class T>auto ve(bool,const vector<T> &vx){cerr << "{\n";for(const T&x:vx)cerr<<"  ",v(x,",");cerr<<"}\n";}template<class T>void v(const vector<T>&vx, string){ve(0,vx);}
template<class T>void v(const set<T>&s,string e){vector<T>z(s.begin(),s.end());v(z,e);}template<class T>void v(const multiset<T>&s,string e){vector<T>z(s.begin(),s.end());v(z,e);}template<class T>void v(const unordered_set<T>&s,string e){vector<T>z(s.begin(),s.end());v(z,e);}template<class T>void v(const deque<T>&s,string e){vector<T>z(s.begin(),s.end());v(z,e);}template<class T>void v(const priority_queue<T>&p,string e){priority_queue<T>q=p;vector<T>z;while(!q.empty()){z.push_back(q.top());q.pop();}v(z,e);}
template<class T,class U>void v(const map<T, U>&m,string e){cerr<<"{"<<(m.empty()?"":"\n");for(const auto&kv:m){cerr<<"  [";v(kv.first,"");cerr<<"] : ";v(kv.second,"");cerr<<"\n";}cerr<<"}"+e;}
template<class T>void _view(int n,string s,T&var){cerr<<"\033[1;32m"<<n<<"\033[0m: \033[1;36m"<<s<<"\033[0m = ";v(var,"\n");}template<class T>void grid(T _){}void grid(const vector<vector<bool>>&vvb){cerr<<"\n";for(const vector<bool>&vb:vvb){for(const bool&b:vb)cerr<<(b?".":"#");cerr<<"\n";}}
void _debug(int, string){}template<typename H,typename... T>void _debug(int n,string S,H h,T... t){int i=0,cnt=0;for(;i<int(S.size());i++){if(S[i]=='(')cnt++;if(S[i]==')')cnt--;if(cnt==0&&S[i]==',')break;}if(i==int(S.size()))i=-1;if(i==-1)_view(n,S,h);else {string s1=S.substr(0,i);string s2=S.substr(i+2);if(s2=="\"grid\"")cerr<<n<<": "<<s1<<" = ",grid(h);else _view(n,s1,h),_debug(n,s2,t...);}}}
template<class T>bool chmax(T&a,const T&b){if(a<b){a=b;return 1;}return 0;}template<class T>bool chmin(T&a,const T&b){if(b<a){a=b;return 1;}return 0;}
#ifdef ONLINE_JUDGE
#define debug(...)
#else
#define debug(...)viewer::_debug(__LINE__,#__VA_ARGS__,__VA_ARGS__)
#endif  // clang-format on

// clang-format off
// https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a
template<int MOD> struct Fp{long long val;constexpr Fp(long long v=0)noexcept:val(v%MOD){if(val<0)val+=MOD;}static constexpr int getmod(){return MOD;}constexpr Fp operator-()const noexcept{return val?MOD-val:0;}
constexpr Fp operator+(const Fp&r)const noexcept{return Fp(*this)+=r;}constexpr Fp operator-(const Fp&r)const noexcept{return Fp(*this)-=r;}constexpr Fp operator*(const Fp&r)const noexcept{return Fp(*this)*=r;}constexpr Fp operator/(const Fp&r)const noexcept{return Fp(*this)/=r;}
constexpr Fp operator++(int)noexcept{val+=1;if(val>=MOD)val-=MOD;return*this;}constexpr Fp operator--(int)noexcept{val-=1;if(val<0)val+=MOD;return*this;}
constexpr Fp&operator+=(const Fp&r)noexcept{val+=r.val;if(val>=MOD)val-=MOD;return*this;}constexpr Fp&operator-=(const Fp&r)noexcept{val-=r.val;if(val<0)val+=MOD;return*this;}constexpr Fp&operator*=(const Fp&r)noexcept{val=val*r.val%MOD;return*this;}constexpr Fp&operator/=(const Fp&r)noexcept{long long a=r.val,b=MOD,u=1,v=0;while(b){long long t=a/b;a-=t*b;swap(a,b);u-=t*v;swap(u,v);}val=val*u%MOD;if(val<0)val+=MOD;return*this;}
constexpr bool operator<(const Fp&r)const noexcept{return this->val<r.val;}constexpr bool operator>(const Fp&r)const noexcept{return this->val>r.val;}constexpr bool operator<=(const Fp&r)const noexcept{return this->val<=r.val;}constexpr bool operator>=(const Fp&r)const noexcept{return this->val>=r.val;}constexpr bool operator==(const Fp&r)const noexcept{return this->val==r.val;}constexpr bool operator!=(const Fp&r)const noexcept{return this->val!=r.val;}
friend constexpr ostream& operator<<(ostream&os,const Fp<MOD>&x)noexcept{return os<<x.val;}};using mint=Fp<998244353>;vector<mint>mod_factorial={mint(1)};
mint modpow(mint base,long long exp){mint ret=1;if(base==0&&exp==0)cerr<<"\033[1;31mWARNING: 0^0 is a mathematical expression with no agreed-upon value.\033[0m"<<endl;while(exp>0){if(exp&1)ret*=base;base*=base;exp>>=1;}return ret;}
mint modinv(mint base)noexcept{return modpow(base,base.getmod()-2);}
/*mod must be a prime number*/mint modsqrt(mint a){long long p=mint::getmod();if(a<2)return a;if(modpow(a,(p-1)>>1)!=1)return -1;mint b=1,one=1;while(modpow(b,(p-1)>>1)==1)b+=one;long long m=p-1,e=0;while(m%2==0)m>>=1,e++;mint x=modpow(a,(m-1)>>1);mint y=a*x*x;x*=a;mint z=modpow(b,m);while(y!=1){long long j=0;mint t=y;while(t!=one)j++,t*=t;z=modpow(z,1ll<<(e-j-1));x*=z;z*=z;y*=z;e=j;}return x;}
/*min x s.t. a^x ≡ b (mod m) or -1*/mint modlog(mint a, mint b){long long m=mint::getmod();long long lo=-1,hi=m;while(hi-lo>1){long long mi=(lo+hi)>>1;if(mi*mi>=m)hi=mi;else lo=mi;}long long sqrtM=hi;map<mint,long long>apow;mint rem=a;for(long long r=1;r<sqrtM;r++){if(apow.find(rem)==apow.end())apow[rem]=r;rem*=a;}mint A=modpow(modinv(a),sqrtM);rem=b;for(mint q=0;q<sqrtM;q++){if(rem==1&&q>0)return q*sqrtM;if(apow.find(rem)!=apow.end())return q*sqrtM+apow[rem];rem*=A;}return -1;}
mint modfact(int n){if(int(mod_factorial.size())<=n){for(int i=mod_factorial.size();i<=n;i++){mint next=mod_factorial.back()*i;mod_factorial.push_back(next);}}return mod_factorial[n];}
mint nCk(int n,int k){if(k<0||n<k)return mint(0);return modfact(n)*modinv(modfact(k))*modinv(modfact(n-k));}  // clang-format on

// clang-format off
// https://ei1333.github.io/library/math/fps/formal-power-series-friendly-ntt.cpp
struct NumberTheoreticTransformFriendlyModInt {
    static vector<mint> roots, iroots, rate3, irate3;
    static int max_base;
    NumberTheoreticTransformFriendlyModInt() = default;
    static void init() {
        if (roots.empty()) {
            const unsigned mod = mint::getmod();
            assert(mod >= 3 && mod % 2 == 1);
            auto tmp = mod - 1;
            max_base = 0;
            while (tmp % 2 == 0) tmp >>= 1, max_base++;
            mint root = 2;
            while (modpow(root, (mod - 1) >> 1) == 1) root += 1;
            assert(modpow(root, mod - 1) == 1);
            roots.resize(max_base + 1);
            iroots.resize(max_base + 1);
            rate3.resize(max_base + 1);
            irate3.resize(max_base + 1);
            roots[max_base] = modpow(root, (mod - 1) >> max_base);
            iroots[max_base] = mint(1) / roots[max_base];
            for (int i = max_base - 1; i >= 0; i--) {
                roots[i] = roots[i + 1] * roots[i + 1];
                iroots[i] = iroots[i + 1] * iroots[i + 1];
            }
            {
                mint prod = 1, iprod = 1;
                for (int i = 0; i <= max_base - 3; i++) {
                    rate3[i] = roots[i + 3] * prod;
                    irate3[i] = iroots[i + 3] * iprod;
                    prod *= iroots[i + 3];
                    iprod *= roots[i + 3];
                }
            }
        }
    }
    static void ntt(vector<mint> &a) {
        init();
        const int n = (int)a.size();
        assert((n & (n - 1)) == 0);
        int h = __builtin_ctz(n);
        assert(h <= max_base);
        int len = 0;
        mint imag = roots[2];
        if (h & 1) {
            int p = 1 << (h - 1);
            // mint rot = 1; 注記:元のライブラリではコメントアウトされず
            for (int i = 0; i < p; i++) {
                auto r = a[i + p];
                a[i + p] = a[i] - r;
                a[i] += r;
            }
            len++;
        }
        for (; len + 1 < h; len += 2) {
            int p = 1 << (h - len - 2);
            {  // s = 0
                for (int i = 0; i < p; i++) {
                    auto a0 = a[i];
                    auto a1 = a[i + p];
                    auto a2 = a[i + 2 * p];
                    auto a3 = a[i + 3 * p];
                    auto a1na3imag = (a1 - a3) * imag;
                    auto a0a2 = a0 + a2;
                    auto a1a3 = a1 + a3;
                    auto a0na2 = a0 - a2;
                    a[i] = a0a2 + a1a3;
                    a[i + 1 * p] = a0a2 - a1a3;
                    a[i + 2 * p] = a0na2 + a1na3imag;
                    a[i + 3 * p] = a0na2 - a1na3imag;
                }
            }
            mint rot = rate3[0];
            for (int s = 1; s < (1 << len); s++) {
                int offset = s << (h - len);
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                for (int i = 0; i < p; i++) {
                    auto a0 = a[i + offset];
                    auto a1 = a[i + offset + p] * rot;
                    auto a2 = a[i + offset + 2 * p] * rot2;
                    auto a3 = a[i + offset + 3 * p] * rot3;
                    auto a1na3imag = (a1 - a3) * imag;
                    auto a0a2 = a0 + a2;
                    auto a1a3 = a1 + a3;
                    auto a0na2 = a0 - a2;
                    a[i + offset] = a0a2 + a1a3;
                    a[i + offset + 1 * p] = a0a2 - a1a3;
                    a[i + offset + 2 * p] = a0na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0na2 - a1na3imag;
                }
                rot *= rate3[__builtin_ctz(~s)];
            }
        }
    }
    static void intt(vector<mint> &a, bool f = true) {
        init();
        const int n = (int)a.size();
        assert((n & (n - 1)) == 0);
        int h = __builtin_ctz(n);
        assert(h <= max_base);
        int len = h;
        mint iimag = iroots[2];
        for (; len > 1; len -= 2) {
            int p = 1 << (h - len);
            {  // s = 0
                for (int i = 0; i < p; i++) {
                    auto a0 = a[i];
                    auto a1 = a[i + 1 * p];
                    auto a2 = a[i + 2 * p];
                    auto a3 = a[i + 3 * p];
                    auto a2na3iimag = (a2 - a3) * iimag;
                    auto a0na1 = a0 - a1;
                    auto a0a1 = a0 + a1;
                    auto a2a3 = a2 + a3;
                    a[i] = a0a1 + a2a3;
                    a[i + 1 * p] = (a0na1 + a2na3iimag);
                    a[i + 2 * p] = (a0a1 - a2a3);
                    a[i + 3 * p] = (a0na1 - a2na3iimag);
                }
            }
            mint irot = irate3[0];
            for (int s = 1; s < (1 << (len - 2)); s++) {
                int offset = s << (h - len + 2);
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                for (int i = 0; i < p; i++) {
                    auto a0 = a[i + offset];
                    auto a1 = a[i + offset + 1 * p];
                    auto a2 = a[i + offset + 2 * p];
                    auto a3 = a[i + offset + 3 * p];
                    auto a2na3iimag = (a2 - a3) * iimag;
                    auto a0na1 = a0 - a1;
                    auto a0a1 = a0 + a1;
                    auto a2a3 = a2 + a3;
                    a[i + offset] = a0a1 + a2a3;
                    a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
                    a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
                    a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
                }
                irot *= irate3[__builtin_ctz(~s)];
            }
        }
        if (len >= 1) {
            int p = 1 << (h - 1);
            for (int i = 0; i < p; i++) {
                auto ajp = a[i] - a[i + p];
                a[i] += a[i + p];
                a[i + p] = ajp;
            }
        }
        if (f) {
            mint inv_sz = mint(1) / n;
            for (int i = 0; i < n; i++) a[i] *= inv_sz;
        }
    }
    static vector<mint> multiply(vector<mint> a, vector<mint> b) {
        int need = a.size() + b.size() - 1;
        int nbase = 1;
        while ((1 << nbase) < need) nbase++;
        int sz = 1 << nbase;
        a.resize(sz, 0);
        b.resize(sz, 0);
        ntt(a);
        ntt(b);
        mint inv_sz = mint(1) / sz;
        for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        intt(a, false);
        a.resize(need);
        return a;
    }
};

vector<mint> NumberTheoreticTransformFriendlyModInt::roots = vector<mint>();
vector<mint> NumberTheoreticTransformFriendlyModInt::iroots = vector<mint>();
vector<mint> NumberTheoreticTransformFriendlyModInt::rate3 = vector<mint>();
vector<mint> NumberTheoreticTransformFriendlyModInt::irate3 = vector<mint>();
int NumberTheoreticTransformFriendlyModInt::max_base = 0;

template <typename T>
struct FormalPowerSeriesFriendlyNTT : vector<T> {
    using vector<T>::vector;
    using P = FormalPowerSeriesFriendlyNTT;
    using NTT = NumberTheoreticTransformFriendlyModInt;
    P pre(int deg)const{return P(begin(*this),begin(*this)+min((int)this->size(),deg));}
    P rev(int deg=-1)const{P ret(*this);if(deg!=-1)ret.resize(deg,T(0));reverse(begin(ret),end(ret));return ret;}
    void shrink(){while(this->size()&&this->back()==T(0))this->pop_back();}
    P operator+(const P&r)const{return P(*this)+=r;}
    P operator+(const T&v)const{return P(*this)+=v;}
    P operator-(const P&r)const{return P(*this)-=r;}
    P operator-(const T&v)const{return P(*this)-=v;}
    P operator*(const P&r)const{return P(*this)*=r;}
    P operator*(const T&v)const{return P(*this)*=v;}
    P operator/(const P&r)const{return P(*this)/=r;}
    P operator%(const P&r)const{return P(*this)%=r;}
    P &operator+=(const P&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;}
    P &operator-=(const P&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;}
    // https://judge.yosupo.jp/problem/convolution_mod
    P &operator*=(const P&r){if(this->empty()||r.empty()){this->clear();return*this;}auto ret=NTT::multiply(*this,r);return*this={begin(ret),end(ret)};}
    P &operator/=(const P&r){if(this->size()<r.size()){this->clear();return*this;}int n=this->size()-r.size()+1;return*this=(rev().pre(n)*r.rev().inv(n)).pre(n).rev(n);}
    P &operator%=(const P&r){*this-=*this/r*r;shrink();return*this;}
    // https://judge.yosupo.jp/problem/division_of_polynomials
    pair<P,P>div_mod(const P&r) {P q=*this/r;P x=*this-q*r;x.shrink();return make_pair(q,x);}
    P operator-()const{P ret(this->size());for(int i=0;i<(int)this->size();i++)ret[i]=-(*this)[i];return ret;}
    P&operator+=(const T&r){if(this->empty())this->resize(1);(*this)[0]+=r;return*this;}
    P&operator-=(const T&r){if(this->empty())this->resize(1);(*this)[0]-=r;return*this;}
    P&operator*=(const T&v){for(int i=0;i<(int)this->size();i++)(*this)[i]*=v;return*this;}
    P dot(P r)const{P ret(min(this->size(),r.size()));for(int i=0;i<(int)ret.size();i++)ret[i]=(*this)[i]*r[i];return ret;}
    P operator>>(int sz)const{if((int)this->size()<=sz)return{};P ret(*this);ret.erase(ret.begin(),ret.begin()+sz);return ret;}
    P operator<<(int sz)const{P ret(*this);ret.insert(ret.begin(), sz, T(0));return ret;}
    //operator(x): f(x)の値を評価して返す O(n)
    T operator()(T x) const{T r=0,w=1;for(auto&v:*this){r+=w*v;w*=x;}return r;}
    // diff(): f'(x)を返す O(n)
    P diff() const {
        const int n = (int)this->size();
        P ret(max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }
    // integral(): ∫f(x)dxを返す O(n)
    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }
    // inv(): 1/f(x)を返す f(0)!=0を要求する deg==-1の時、同じ次数で打ち切る
    // https://judge.yosupo.jp/problem/inv_of_formal_power_series
    P inv(int deg = -1) const {
        assert(((*this)[0]) != T(0));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P res(deg);
        res[0] = {T(1) / (*this)[0]};
        for (int d = 1; d < deg; d <<= 1) {
            P f(2 * d), g(2 * d);
            for (int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];
            for (int j = 0; j < d; j++) g[j] = res[j];
            NTT::ntt(f);
            NTT::ntt(g);
            f = f.dot(g);
            NTT::intt(f);
            for (int j = 0; j < d; j++) f[j] = 0;
            NTT::ntt(f);
            for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
            NTT::intt(f);
            for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
        }
        return res;
    }
    // log(): logf(x)を返す f(0)==1を要求する deg==-1の時、同じ次数で打ち切る
    // https://judge.yosupo.jp/problem/log_of_formal_power_series
    P log(int deg = -1) const {
        assert((*this)[0] == T(1));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }
    // sqrt(): √f(x)(i.e. g(x) s.t. g(x)*g(x)==f(x))を返す 存在しない場合は空配列を返す deg==-1の時、同じ次数で打ち切る
    // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
    P sqrt(int deg = -1, const function<T(T)> &get_sqrt = [](T y) { return modsqrt(y); }) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++) {
                if ((*this)[i] != T(0)) {
                    if (i & 1) return {};
                    if (deg - i / 2 <= 0) break;
                    auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
                    if (ret.empty()) return {};
                    ret = ret << (i / 2);
                    if ((int)ret.size() < deg) ret.resize(deg, T(0));
                    return ret;
                }
            }
            return P(deg, 0);
        }
        auto sqr = T(get_sqrt((*this)[0]));
        if (sqr * sqr != (*this)[0]) return {};
        P ret{sqr};
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
        }
        return ret.pre(deg);
    }
    P sqrt(const function<T(T)> &get_sqrt, int deg = -1) const {
        return sqrt(deg, get_sqrt);
    }
    // exp(): exp(f(x))を返す f(0)=0を要求する deg==-1の時、同じ次数で打ち切る
    // https://judge.yosupo.jp/problem/exp_of_formal_power_series
    P exp(int deg = -1) const {
        if (deg == -1) deg = this->size();
        assert((*this)[0] == T(0));
        P inv;
        inv.reserve(deg + 1);
        inv.push_back(T(0));
        inv.push_back(T(1));
        auto inplace_integral = [&](P &F) -> void {
            const int n = (int)F.size();
            auto mod = T::getmod();
            while ((int)inv.size() <= n) {
                int i = inv.size();
                inv.push_back((-inv[mod % i]) * (mod / i));
            }
            F.insert(begin(F), T(0));
            for (int i = 1; i <= n; i++) F[i] *= inv[i];
        };
        auto inplace_diff = [](P &F) -> void {
            if (F.empty()) return;
            F.erase(begin(F));
            T coeff = 1, one = 1;
            for (int i = 0; i < (int)F.size(); i++) {
                F[i] *= coeff;
                coeff += one;
            }
        };
        P 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);
            NTT::ntt(y);
            z1 = z2;
            P z(m);
            for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
            NTT::intt(z);
            fill(begin(z), begin(z) + m / 2, T(0));
            NTT::ntt(z);
            for (int i = 0; i < m; ++i) z[i] *= -z1[i];
            NTT::intt(z);
            c.insert(end(c), begin(z) + m / 2, end(z));
            z2 = c;
            z2.resize(2 * m);
            NTT::ntt(z2);
            P x(begin(*this), begin(*this) + min<int>(this->size(), m));
            inplace_diff(x);
            x.push_back(T(0));
            NTT::ntt(x);
            for (int i = 0; i < m; ++i) x[i] *= y[i];
            NTT::intt(x);
            x -= b.diff();
            x.resize(2 * m);
            for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0);
            NTT::ntt(x);
            for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
            NTT::intt(x);
            x.pop_back();
            inplace_integral(x);
            for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
                x[i] += (*this)[i];
            fill(begin(x), begin(x) + m, T(0));
            NTT::ntt(x);
            for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
            NTT::intt(x);
            b.insert(end(b), begin(x) + m, end(x));
        }
        return P{begin(b), begin(b) + deg};
    }
    // pow(k): f^k(x)を返す deg==-1の時、同じ次数で打ち切る
    // https://judge.yosupo.jp/problem/pow_of_formal_power_series
    P pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P ret = (((*this * rev) >> i).log() * k).exp() *
                        (modpow((*this)[i],k));
                if (i * k > deg) return P(deg, T(0));
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, T(0));
                return ret;
            }
        }
        return *this;
    }
    // mod_pow(k,g): f^k(x) (mod g(x))を返す O(nlogklogdeg(f))
    P mod_pow(int64_t k, P g) const {
        P modinv = g.rev().inv();
        auto get_div = [&](P base) {
            if (base.size() < g.size()) {
                base.clear();
                return base;
            }
            int n = base.size() - g.size() + 1;
            return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
        };
        P x(*this), ret{1};
        while (k > 0) {
            if (k & 1) {
                ret *= x;
                ret -= get_div(ret) * g;
                ret.shrink();
            }
            x *= x;
            x -= get_div(x) * g;
            x.shrink();
            k >>= 1;
        }
        return ret;
    }
    //taylor_shift(c): g(x)=f(x+c)を満たすg(x)を返す
    // https://judge.yosupo.jp/problem/polynomial_taylor_shift
    P taylor_shift(T c) const {
        int n = (int)this->size();
        vector<T> fact(n), rfact(n);
        fact[0] = rfact[0] = T(1);
        for (int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i);
        rfact[n - 1] = T(1) / fact[n - 1];
        for (int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i);
        P p(*this);
        for (int i = 0; i < n; i++) p[i] *= fact[i];
        p = p.rev();
        P bs(n, T(1));
        for (int i = 1; i < n; i++)
            bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
        p = (p * bs).pre(n);
        p = p.rev();
        for (int i = 0; i < n; i++) p[i] *= rfact[i];
        return p;
    }
};
// clang-format on

using FPS = FormalPowerSeriesFriendlyNTT<mint>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<mint> As(N - 1);
    vector<mint> fact(N),rfact(N);
    fact[0] = rfact[0] = 1;
    for (int i = 1; i < N; i++) fact[i] = fact[i - 1]*(mint)i;
    rfact[N - 1] = (mint)1/fact[N - 1];
    for (int i = N - 1; i > 1; i--) rfact[i - 1] = rfact[i] * mint(i);
    for (int i = 0;i<N - 1; i++){
        As[i] = (mint)(i + 1)*rfact[i];
    }
    FPS fps_A(As.begin(), As.end());
    FPS ans = fps_A.pow(N);
    ans[N - 2] *= fact[N - 2];
    ans[N - 2] /= modpow(N,N - 2);
    cout << ans[N - 2] << endl;
}