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

struct Montgomery{
    //2^62未満&奇数modのみ.
    //初めにsetmodする.
    using u64 = uint64_t;
    using u128 = __uint128_t;
 
    private:
    static u64 mod,N2,Rsq; //N*N2≡1(mod N);
    //Rsq = R^2modN; R=2^64.
    u64 v = 0;
    public:
    long long val(){return reduce(v);}
    static u64 getmod(){return mod;}
    static void setmod(u64 m){
        assert(m<(1LL<<62)&&(m&1));
        mod = m; N2 = mod;
        for(int i=0; i<5; i++) N2 *= 2-N2*mod;
        Rsq = (-u128(mod))%mod;
    }
    //reduce = T*R^-1modNを求める.
    u64 reduce(const u128 &T){
        //T*R^-1≡(T+(T*(-N2))modR*N)/R 2N未満なので-N必要かだけで良い.
        u64 ret = (T+u128(((u64)T)*(-N2))*mod)>>64;
        if(ret >= mod) ret -= mod;
        return ret;
    }
    //初期値<mod. 初めにw*R modN...->reduce(R^2)でok.
    Montgomery(){v = 0;} Montgomery(long long w):v(reduce(u128(w)*Rsq)){}
 
    Montgomery& operator=(const Montgomery &b) = default;
    Montgomery operator-()const{return Montgomery()-Montgomery(*this);}
    Montgomery operator+(const Montgomery &b)const{return Montgomery(*this)+=b;}
    Montgomery operator-(const Montgomery &b)const{return Montgomery(*this)-=b;}
    Montgomery operator*(const Montgomery &b)const{return Montgomery(*this)*=b;}
    Montgomery operator/(const Montgomery &b)const{return Montgomery(*this)/=b;}
    Montgomery& operator+=(const Montgomery &b){
        v += b.v;
        if(v >= mod) v -= mod;
        return (*this);
    }
    Montgomery& operator-=(const Montgomery &b){
        v += mod-b.v;
        if(v >= mod) v -= mod;
        return (*this);
    }
    Montgomery& operator*=(const Montgomery &b){
        v = reduce(u128(v)*b.v);
        return (*this);
    }
    Montgomery& operator/=(const Montgomery &b){
        (*this) *= b.inv();
        return (*this);
    }
    Montgomery pow(u64 b)const{
        Montgomery ret = 1,p = (*this);
        while(b){
            if(b&1) ret *= p;
            p *= p; b >>= 1;
        }
        return ret;
    }
    Montgomery inv()const{return pow(mod-2);}
 
    bool operator!=(const Montgomery &b)const{return v!=b.v;}
    bool operator==(const Montgomery &b)const{return v==b.v;}
};
typename Montgomery::u64 Montgomery::mod,Montgomery::N2,Montgomery::Rsq;
using mint = Montgomery;

namespace to_fold{ //纏めて折り畳むためのやつ 苦労したが結局ほぼACLの写経.
__int128_t safemod(__int128_t a,long long m){a %= m; if(a < 0) a += m; return a;}
pair<long long,long long> invgcd(long long a,long long b){
    //return {gcd(a,b),x} (xa≡g(mod b))
    a = safemod(a,b);
    if(a == 0) return {b,0};
    long long x = 0,y = 1,memob = b;
    while(a){
        long long q = b/a;
        b -= a*q;
        swap(x,y); y -= q*x;
        swap(a,b);
    }
    if(x < 0) x += memob/b;
    return {b,x};
}
long long Garner(vector<long long> &A,vector<long long> &M){
    __int128_t mulM = 1,x = A.at(0)%M.at(0); //Mの要素のペア互いに素必須.
    for(int i=1; i<A.size(); i++){
        //assert(gcd(mulM,M.at(i-1)) == 1);
        mulM *= M.at(i-1); //2乗がオーバーフローする時__int128_t
        long long t = safemod((A.at(i)-x)*invgcd(mulM,M.at(i)).second,M.at(i));
        x += t*mulM;
    }
    return x%mint::getmod();
}
int countzero(unsigned long long x){
    if(x == 0) return 64;
    else return __popcount((x&-x)-1);
}

struct fftinfo{
    private:
    long long checkmod;
    public:
    long long getmod(){return checkmod;}
    vector<mint> root,iroot,rate2,irate2,rate3,irate3;
    fftinfo(mint g){
        checkmod = mint::getmod();
        int rank2 = countzero(mint::getmod()-1);
        root.resize(rank2+1),iroot = root;
        rate2.resize(max(0,rank2-2+1)); irate2 = rate2;
        rate3.resize(max(0,rank2-3+1)); irate3 = rate3;

        root[rank2] = g.pow((mint::getmod()-1)>>rank2);
        iroot[rank2] = root[rank2].inv();
        for(int i=rank2-1; i>=0; i--){
            root[i] = root[i+1]*root[i+1];
            iroot[i] = iroot[i+1]*iroot[i+1];
        }
        mint mul = 1,imul = 1;
        for(int i=0; i<=rank2-2; i++){
            rate2[i] = root[i+2]*mul;
            irate2[i] = iroot[i+2]*imul;
            mul *= iroot[i+2],imul *= root[i+2];
        }
        mul = 1,imul = 1;
        for(int i=0; i<=rank2-3; i++){
            rate3[i] = root[i+3]*mul;
            irate3[i] = iroot[i+3]*imul;
            mul *= iroot[i+3],imul *= root[i+3];
        }
    }
};
mint findroot(){
    if(mint::getmod() == 998244353) return mint(3);
    else if(mint::getmod() == 754974721) return mint(11);
    else if(mint::getmod() == 167772161) return mint(3);
    else if(mint::getmod() == 469762049) return mint(3);
    assert(false); //バグあったので.
}
fftinfo info(3);
void NTT(vector<mint> &A){
    long long Mod = mint::getmod();
    if(info.getmod() != Mod) info = fftinfo(findroot());
    int N = A.size(),ln = countzero(N);
    int dep = 0;
    while(dep < ln){
        if(ln-dep == 1){
            int p = 1<<(ln-dep-1);
            mint rot = 1;
            for(int o=0; o<(1<<dep); o++){
                int offset = o<<(ln-dep);
                for(int i=0; i<p; i++){
                    mint l = A.at(i+offset),r = A.at(i+offset+p)*rot;
                    A.at(i+offset) = l+r; A.at(i+offset+p) = l-r;
                }
                if(o+1 != (1<<dep)) rot *= info.rate2[countzero(~(unsigned int)o)];
            }
            dep++;
        }
        else{
            int p = 1<<(ln-dep-2);
            mint rot = 1,imag = info.root[2];
            for(int o=0; o<(1<<dep); o++){
                mint rot2 = rot*rot,rot3 = rot2*rot;
                int offset = o<<(ln-dep);
                for(int i=0; i<p; i++){
                    auto mod2 = 1ULL*Mod*Mod;
                    auto a0 = 1ULL*A.at(i+offset).val();
                    auto a1 = 1ULL*A.at(i+offset+p).val()*rot.val();
                    auto a2 = 1ULL*A.at(i+offset+p+p).val()*rot2.val();
                    auto a3 = 1ULL*A.at(i+offset+p+p+p).val()*rot3.val();
                    auto a1m2a3im = 1ULL*(a1+mod2-a3+Mod)%Mod*imag.val();
                    auto m2a2 = mod2-a2;
                    A.at(i+offset) = (long long)((a0+a2+a1+a3)%Mod);
                    A.at(i+offset+p) = (long long)((a0+a2+(2*mod2-(a1+a3)))%Mod);
                    A.at(i+offset+p+p) = (long long)((a0+m2a2+a1m2a3im)%Mod);
                    A.at(i+offset+p+p+p) = (long long)((a0+m2a2+(mod2-a1m2a3im))%Mod);
                }
                if(o+1 != (1<<dep)) rot *= info.rate3[countzero(~(unsigned int)o)];
            }
            dep += 2;
        }
    }
}
void INTT(vector<mint> &A){
    long long Mod = mint::getmod();
    if(info.getmod() != Mod) info = fftinfo(findroot());
    int N = A.size(),ln = countzero(N),dep = ln;
    while(dep){
        if(dep == 1){
            int p = 1<<(ln-dep);
            mint irot = 1;
            for(int o=0; o<(1<<(dep-1)); o++){
                int offset = o<<(ln-dep+1);
                for(int i=0; i<p; i++){
                    mint l = A.at(i+offset),r = A.at(i+offset+p);
                    A.at(i+offset) = l+r;
                    A.at(i+offset+p) = (long long)((unsigned long long)((Mod+l.val()-r.val())*irot.val())%Mod);
                }
                if(o+1 != (1<<(dep-1))) irot *= info.irate2[countzero(~(unsigned int)o)];
            }
            dep--;
        }
        else{
            int p = 1<<(ln-dep);
            mint irot = 1,iimag = info.iroot[2];
            for(int o=0; o<(1<<(dep-2)); o++){
                mint irot2 = irot*irot,irot3 = irot2*irot;
                int offset = o<<(ln-dep+2);
                for(int i=0; i<p; i++){
                    auto a0 = 1ULL*A.at(i+offset).val(),a1 = 1ULL*A.at(i+offset+p).val();
                    auto a2 = 1ULL*A.at(i+offset+p+p).val(),a3 = 1ULL*A.at(i+offset+p+p+p).val();
                    auto gotyagotya = 1ULL*((Mod+a2-a3)*iimag.val()%Mod);
                    A.at(i+offset) = (long long)((a0+a1+a2+a3)%Mod);
                    A.at(i+offset+p) = (long long)((a0+(Mod-a1)+gotyagotya)*irot.val()%Mod);
                    A.at(i+offset+p+p) = (long long)((a0+a1+(Mod-a2)+(Mod-a3))*irot2.val()%Mod);
                    A.at(i+offset+p+p+p) = (long long)((a0+(Mod-a1)+(Mod-gotyagotya))*irot3.val()%Mod);
                }
                if(o+1 != (1<<(dep-2))) irot *= info.irate3[countzero(~(unsigned int)o)];
            }
            dep -= 2;
        }
    }
}
vector<mint> convolution(vector<mint> &A,vector<mint> &B){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1,N = 1;
    if(siza == 0 || sizb == 0) return {};
    if(min(siza,sizb) <= 50){ //naive.
        vector<mint> ret(sizc);
        for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);
        return ret;
    }

    while(N <= sizc) N <<= 1;
    vector<mint> ca = A,cb = B;
    ca.resize(N),cb.resize(N);
    assert((mint::getmod()-1)%N == 0);

    mint root = findroot();
    NTT(ca); NTT(cb);
    for(int i=0; i<N; i++) ca.at(i) *= cb.at(i);
    INTT(ca); ca.resize(sizc);

    mint divN = mint(N).inv();
    for(int i=0; i<sizc; i++) ca.at(i) *= divN;
    return ca;
}
vector<long long> convolution_ll(vector<long long> &A,vector<long long> &B){ //long longに収まる範囲.
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
    vector<long long> ret(sizc);
    if(min(siza,sizb) <= 200){ //naive 200はやばい?.
        for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);
        return ret;
    }

    unsigned long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    unsigned long long m1m2 = mod1*mod2,m2m3 = mod2*mod3,m3m1 = mod3*mod1,m1m2m3 = mod1*mod2*mod3;
    unsigned long long i1 = invgcd(m2m3,mod1).second,i2 = invgcd(m3m1,mod2).second,i3 = invgcd(m1m2,mod3).second;
    assert(sizc <= (1<<24));

    mint::setmod(mod1);
    vector<mint> a(siza),b(sizb);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod1;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod1;
    vector<mint> C1 = convolution(a,b);
    mint::setmod(mod2);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod2;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod2;
    vector<mint> C2 = convolution(a,b);
    mint::setmod(mod3);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod3;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod3;
    vector<mint> C3 = convolution(a,b);

    vector<unsigned long long> offset = {0,0,m1m2m3,2*m1m2m3,3*m1m2m3};
    for(int i=0; i<sizc; i++){
        unsigned long long x = 0;
        x += (C1.at(i).val()*i1)%mod1*m2m3;
        x += (C2.at(i).val()*i2)%mod2*m3m1;
        x += (C3.at(i).val()*i3)%mod3*m1m2;
        long long diff = C1.at(i).val()-((long long)x+(long long)mod1)%mod1;
        if(diff < 0) diff += mod1;
        x -= offset.at(diff%5);
        ret.at(i) = x;
    }
    return ret;
}
vector<mint> convolution_llmod(vector<mint> &A,vector<mint> &B,long long memomod){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
    vector<mint> ret(sizc);
    if(min(siza,sizb) <= 200){
        for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);
        return ret;
    }

    long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    assert(sizc <= (1<<24));

    mint::setmod(mod1);
    vector<mint> a(siza),b(sizb);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).val()%mod1;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).val()%mod1;
    vector<mint> C1 = convolution(a,b);
    mint::setmod(mod2);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).val()%mod2;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).val()%mod2;
    vector<mint> C2 = convolution(a,b);
    mint::setmod(mod3);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).val()%mod3;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).val()%mod3;
    vector<mint> C3 = convolution(a,b);

    mint::setmod(memomod);
    for(int i=0; i<sizc; i++){
        vector<long long> A = {C1.at(i).val(),C2.at(i).val(),C3.at(i).val()};
        vector<long long> M = {mod1,mod2,mod3};
        ret.at(i) = Garner(A,M);
    }
    return ret;
}
vector<int> convolution_int(vector<int> &A,vector<int> &B){ //intに収まる範囲.
    if(A.size() == 0 || B.size() == 0) return {};
    vector<int> ret;
    if(min(A.size(),B.size()) <= 50){
        ret.resize(A.size()+B.size()-1);
        for(int i=0; i<A.size(); i++) for(int k=0; k<B.size(); k++) ret.at(i+k) += A.at(i)*B.at(k);
    }
    else{
        vector<mint> X,Y,Z;
        for(auto &a : A) X.push_back(a);
        for(auto &b : B) Y.push_back(b);
        Z = convolution(X,Y);
        for(auto &z : Z) ret.push_back(z.val());
    }
    return ret;
}
}
using namespace to_fold;

template<typename T> //実質mintだけ?.
struct FormalPowerSeries:vector<T>{ //NTT-friendly素数だけ じゃなくてもいいけど全部書き直せ!.
    using vector<T>::vector;
    using fps = FormalPowerSeries;
 
    //重要なところは某のほぼパクリ.
    fps operator++(){*this += 1; return *this;}
    fps operator--(){*this -= 1; return *this;}
    fps operator++(int){*this += 1; return *this;}
    fps operator--(int){*this -= 1; return *this;}
    fps operator+(const fps &b) const {return fps(*this)+=b;}
    fps operator+(const T &b) const {return fps(*this)+=b;}
    fps operator-(const fps &b) const {return fps(*this)-=b;}
    fps operator-(const T &b) const {return fps(*this)-=b;}
    fps operator*(const fps &b){return fps(*this)*=b;}
    fps operator*(const T &b) const {return fps(*this)*=b;}
    fps operator/(const fps &b) const {return fps(*this)/=b;}
    fps operator%(const fps &b) const {return fps(*this)%=b;}
    fps operator>>(const unsigned int b) const {return fps(*this)>>=b;}
    fps operator<<(const unsigned int b) const {return fps(*this)<<=b;}
    fps operator-() const {
        fps ret = (*this);
        for(auto &v : ret) v = -v;
        return ret;
    }
    bool operator==(const fps &b)const{
        if((*this).size() != b.size()) return false;
        for(int i=0; i<(*this).size(); i++) if((*this).at(i) != b.at(i)) return false;
        return true;
    }
    bool operator!=(const fps &b)const{return !((*this)==b);}
 
    fps &operator+=(const fps &b){ //Cix^i = (Ai+Bi)x^i. O(n).
        if((*this).size() < b.size()) (*this).resize(b.size(),0);
        for(int i=0; i<b.size(); i++) (*this).at(i) += b.at(i);
        return *this;
    }
    fps &operator+=(const T &b){ //x^0の係数に+b O(1).
        if((*this).size() == 0) (*this).resize(1);
        (*this).at(0) += b;
        return *this;
    }
    fps &operator-=(const fps &b){ //Cix^i = (Ai-Bi)x^i. O(n).
        int n = b.size();
        if((*this).size() < n) (*this).resize(n,0);
        for(int i=0; i<n; i++) (*this).at(i) -= b.at(i);
        return *this;
    }
    fps &operator-=(const T &b){ //x^0の係数に-b O(1).
        if((*this).size() == 0) (*this).resize(1);
        (*this).at(0) -= b;
        return *this;
    }
    fps &operator*=(const fps &b){ //C[i+k]x^(i+k) = Aix^i+Bkx^k. O(nlogn).
        vector<T> f,g;
        for(auto v : (*this)) f.emplace_back(v);
        for(auto v : b) g.emplace_back(v);
        vector<T> ret;
        if(mint::getmod() == 998244353) ret = convolution(f,g); //型を仕方なく合わせる C++わからん.
        else ret = convolution_llmod(f,g,mint::getmod()); //modがNTT-friendlyじゃない時用 直すのだるい　998以外はとりあえずこっち.
        (*this).resize(ret.size());
        for(int i=0; i<ret.size(); i++) (*this).at(i) = ret.at(i);
        return (*this);
    }
    fps &operator*=(const T &b){ //x^iの係数に*b O(n).
        for(auto &v : (*this)) v *= b; 
        return *this;
    }
    fps &operator/=(const T &b){ //x^iの係数に/b O(logmod+n).
        T mul = b.inv();
        for(auto &v : (*this)) v *= mul;
        return *this;
    }
    fps &operator>>=(const unsigned int &b){//b<0は対象外. 先頭b項を削除. O(n)
        if((*this).size() <= b) (*this).clear();
        else (*this).erase((*this).begin(),(*this).begin()+b);
        return *this;
    }    
    fps &operator<<=(const unsigned int &b){//b<0は対象外. 先頭b項に0を挿入. O(n)
        (*this).insert((*this).begin(),b,0);
        return *this;
    }   
    fps &operator%=(const fps &b){ //多項式の余り. O(nlogn)
        (*this) -= (*this)/b*b;
        del0();
        return (*this);
    }
    fps &operator/=(const fps &b){ //多項式としての除算 O(nlogn).
        assert(b.size() > 0); //分母の末尾0は駄目.
        T check = b.back(); assert(check != 0);
        long long mod = mint::getmod();
        del0(); //分子の末尾0は消して許容.
        if((*this).size() < b.size()){
            (*this).clear();
            return *this;
        }
        int n = (*this).size()-b.size()+1;
        if(b.size() <= 64){ //愚直.
            fps G(b);
            assert(G.size() > 0);
            T div = G.back().inv();
            for (auto &v : G) v *= div;
            int deg = (*this).size()-G.size()+1;
            fps Q(deg);
            for(int i=deg-1; i>=0; i--) {
                Q[i] = (*this).at(i+G.size()-1);
                for(int k=0; k<G.size(); k++) (*this).at(i+k) -= Q.at(i)*G.at(k);
            }
            (*this) = Q*div; (*this).resize(n,0);
            return *this;
        }
        //rev(f)/rev(g)≡rev(ret)(mod x^n)らしい わお.
        //998244353以外は定数倍悪い方に突っ込む.
        if(mint::getmod() == 998244353) return (*this) = ((*this).rev().prefix(n) * b.rev().inv(n)).prefix(n).rev();
        return (*this) = ((*this).rev().prefix(n) * b.rev().inv2(n)).prefix(n).rev();
    }
 
    fps multi_sparse(const fps &b)const{ //非0が少ない時の掛け算 愚直 O(n*|非0|+m).
        int n = (*this).size(),m = b.size();
        vector<pair<int,T>> P;
        for(int i=0; i<m; i++) if(b.at(i) != 0) P.push_back({i,b.at(i)});
        fps ret(n+m-1);
        for(int i=0; i<n; i++) for(auto [k,v] : P) ret.at(i+k) += (*this).at(i)*v;
        return ret;
    };
    fps inv_sparse(int deg=-1)const{ //非0が少ない時の1/fを返す O(deg*|非0|+m+logmod).
        int n = (*this).size();
        if(deg == -1) deg = n;
        assert((*this).at(0) != 0);
        T div = 1;
        vector<pair<int,T>> P;
        if((*this).at(0) != 1) div = T((*this).at(0)).inv();
        for(int i=1; i<n; i++)  if((*this).at(i) != 0) P.emplace_back(pair{i,(*this).at(i)*div});
 
        fps ret(deg); ret.at(0) = 1;
        for(int i=1; i<deg; i++) for(auto [k,v] : P) if(i >= k) ret.at(i) -= v*ret.at(i-k); //-xが+ret[i-1]に対応.
        if(div != 1) for(auto &v : ret) v *= div;
        return ret;
    }
    fps inv_sparse(const fps &b,int deg = -1)const{ //f/gを返す 1/fでは分母だがこれは分子に注意.
        int n = (*this).size(),m = b.size();
        if(deg == -1) deg = n;
        assert(b.at(0) != 0);
        T div = 1;
        vector<pair<int,T>> P;
        if(b.at(0) != 1) div = T(b.at(0)).inv();
        for(int i=1; i<m; i++) if(b.at(i) != 0) P.emplace_back(pair{i,b.at(i)*div});
 
        fps ret = (*this).prefix(deg);
        for(int i=1; i<deg; i++) for(auto [k,v] : P) if(i >= k) ret.at(i) -= v*ret.at(i-k);
        if(div != 1) for(auto &v : ret) v *= div;
        return ret;
    }
    fps log_sparse(int deg = -1){ //log(f)を返す O(N*非0).
        //logf = ∫(f'/f) inv,1/f*(f')がO(N*非0) 他はO(N).
        assert((*this).size()&&(*this).at(0)==1);
        if(deg == -1) deg = (*this).size();
        fps ret = (*this).diff();
        ret = ((*this).inv_sparse(deg)).multi_sparse(ret);
        return ret.inte().prefix(deg);
    }
    fps exp_sparse(int deg = -1)const{ //exp(f)を返す O(N*非0).
        //(expf)'=(f')*exp(f)より低次から決まる.
        //[x^0]expf=1より左辺のx^0の係数が求まる->expfのx^1の係数が求まる->...
        if(deg == -1) deg = (*this).size();
        fps ret(deg); 
        if((*this).size() == 0){
            if(deg > 0) ret.at(0) = 1;
            return ret;
        }
        assert((*this).at(0) == 0);
        long long mod = mint::getmod();
        if(deg == 1) return fps{1};
        ret.at(0) = 1; ret.at(1) = 1;
        for(int i=2; i<deg; i++) ret.at(i) = (-ret.at(mod%i)*(mod/i));
 
        vector<pair<int,T>> P;
        for(int i=1; i<(*this).size(); i++) if((*this).at(i) != 0) P.emplace_back(pair{i-1,(*this).at(i)*i});
        for(int i=0; i<deg-1; i++){
            T now = 0;
            for(auto [k,v] : P){
                if(i < k) break;
                now += ret.at(i-k)*v;
            }
            ret.at(i+1) *= now;
        }
        return ret;
    }
    fps pow_sparse(long long K,int deg = -1)const{ //f^Kを返す O(N*非0).
        //f^K = Fとする fF'= K*F*f'を使う.
        //[x^0]f=1に因数分解 (ax^i)^Kは別で処理.
        //n次はΣ[i=0~n]fi*F'[n-i]=K*Σ[i=1~n+1]F[n+1-i]*i*fi.
        //左辺のi=n以外移項 f0=1より F'n=K*Σ[i=1~n+1]F[n+1-i]*i*fi-Σ[i=1~n]fi*(n+1-i)*F[n+1-i].
        //Fのn次まで分かっていればF'nが求まりFn+1も求まる F0=1からスタート.
        int n = (*this).size();
        long long mod = mint::getmod();
        if(deg == -1) deg = (*this).size();
        if(K == 0 || deg == 0){
            fps ret(deg);
            if(deg > 0) ret.at(0) = 1;
            return ret;
        }
        for(int t=0; t<n; t++){
            if((*this).at(t) != 0){
                T div = T(1)/(*this).at(t);
                vector<pair<int,T>> P;
                for(int i=t+1; i<n; i++) if((*this).at(i) != 0) P.emplace_back(pair{i-t,(*this).at(i)*div});
                fps ret(deg); ret.at(0) = 1;
                if(deg > 1) ret.at(1) = 1;
                for(int i=2; i<deg; i++) ret.at(i) = (-ret.at(mod%i)*(mod/i));
 
                mint mulK = K%mod;
                for(n=0; n<deg-1; n++){ //ここでnの役割が変わる注意.
                    T now = 0;
                    for(auto [i,v] : P){
                        if(i > n+1) break;
                        if(i > 0 && i<=n+1) now += mulK*ret.at(n+1-i)*i*v;
                        if(i > 0 && i <= n) now -= v*(n+1-i)*ret.at(n+1-i);
                    }
                    ret.at(n+1) *= now;
                }
                ret *= T((*this).at(t)).pow(K);
                return (ret<<(t*K)).prefix(deg);
            }
            if(K >= deg || (t+1)*K >= deg) break;
        }
        return fps(deg,0);
    }
 
    fps diff()const{ //微分 nx^(n-1) = (x^n)' O(n).
        int n = (*this).size();
        if(n <= 1) return {};
        fps ret(n-1);
        T multi = 1;
        for(int i=1; i<n; i++) ret.at(i-1) = (*this).at(i)*multi,multi++;
        return ret;
    }
    fps inte()const{ //積分. 1/(n+1)x^(n+1) = ∫x^n dx O(n).
        int n = (*this).size();
        fps ret(n+1);
        ret.at(0) = 0;
        if(n == 0) return ret;
        long long mod = mint::getmod();
        ret.at(1) = 1;
        for(int i=2; i<=n; i++) ret.at(i) = (-ret.at(mod%i)*(mod/i)); //ここでret[i]=1/iになる.
        for(int i=0; i<n; i++) ret.at(i+1) *= (*this).at(i);
        return ret;
    }
 
    fps inv(int deg=-1)const{ //f*g=1 mod x^degとなるgを求める O(nlogn).
        //g.pre(2m)<- (2g.pre(m)-f*g.pre(m)*g.pre(m))mod x^2mとする.
        //fgm≡1 mod x^mからfg2m≡1 mod x^2mが求まる ダブリング.
        //g2m<- gm-((fgm-1)*gm)を求める.
        if((*this).size() <= 100) return inv_sparse(deg);
        assert((*this).at(0) != 0);
        if(deg == -1) deg = (*this).size();
        fps ret(deg);
        ret.at(0) = T(1)/(*this).at(0); T div2 = T(1)/2,divN = 1;
 
        for(int i=1; i<deg; i<<=1){ //NTT-friendlyじゃないと駄目らしい.
            fps f(2*i),g(2*i); divN *= div2;
            int n = min(2*i,(int)(*this).size());
            for(int k=0; k<n; k++) f.at(k) = (*this).at(k);
            for(int k=0; k<i; k++) g.at(k) = ret.at(k);

            NTT(f),NTT(g);
            for(int k=0; k<2*i; k++) f.at(k) *= g.at(k); //(fgm-1)を計算.
            INTT(f);
            for(int k=0; k<i; k++) f.at(k) = 0; //[m,2m)の項だけにする([0,m)は一致してない).
            for(int k=i; k<2*i; k++) f.at(k) *= divN; //convの後のdivNを忘れない.
            NTT(f);
            for(int k=0; k<2*i; k++) f.at(k) *= g.at(k); //(fgm-1)*gmを計算.
            INTT(f);
            n = min(2*i,deg);
            for(int k=i; k<n; k++) f.at(k) *= divN;
            for(int k=i; k<n; k++) ret.at(k) = -f.at(k); //-(fgm^2-gm)が入る.
        }
        return ret; //ね、簡単でしょ？.
    }
    fps inv2(int deg=-1)const{ //NTT-friendlyじゃなくてもいい代わりに定数が重い convも変える O(nlogn).
        //g.pre(2m)<- (2g.pre(m)-f*g.pre(m)*g.pre(m))mod x^2mとする.
        //fgm≡1 mod x^mからfg2m≡1 mod x^2mが求まる ダブリング.
        //こっちは愚直にやる NTT-friendlyじゃないならllmodのconvolutionに変更しないと使えない.
        if((*this).size() <= 200) return inv_sparse(deg);
        assert((*this).at(0) != 0);
        if(deg == -1) deg = (*this).size();
        fps ret(1); ret.at(0) = T(1)/(*this).at(0);
        for(int i=1; i<deg; i<<=1) ret = (ret+ret-ret*ret*((*this).prefix(i<<1))).prefix(i<<1);
        return ret.prefix(deg);
    }
    fps log(int deg=-1,bool NTTfriendly = false)const{ //logfを求める O(nlogn).
        //log(1-f) = -Σ[n=1~∞](f^n/n)と定義する [x^0]f=1&n<modが条件.
        //(logf)'=f'/f,log(fg)=logf+loggが成り立つ.
        assert((*this).size()&&(*this).at(0)==1);
        if(deg == -1) deg = (*this).size();
        if(NTTfriendly) ((*this).diff()*(*this).inv(deg)).prefix(deg-1).inte(); //∫f'/fから求める.
        return ((*this).diff()*(*this).inv2(deg)).prefix(deg-1).inte();
    }
    fps exp(int deg=-1)const{ //expfを求める O(nlogn).
        //expf=Σ[n=0~∞]f^n/n!と定める [x^0]f=0,n<modが条件.
        //(expf)'= f'expf,exp(f+g)=expf*expg,log(expf)=fを満たす (各々条件は忘れずに).
        //ニュートン法で求める g2m<-gm*(1-log(gm)+f) mod x^2nに更新 納得してない.
        assert((*this).size() == 0 || (*this)[0] == mint(0));
        if (deg == -1) deg = (*this).size();
        long long mod = mint::getmod();
        vector<T> divi; //invと衝突回避用 mintでiの逆元.
        divi.resize(deg*2); divi.at(1) = 1;
        for(int i=2; i<deg*2; i++) divi.at(i) = ((-divi.at(mod%i)))*(mod/i);
        auto integral = [&](fps &f) -> void { //inplaceで積分.
            int n = f.size();
            f.insert(f.begin(),0);
            for(int i=1; i<=n; i++) f.at(i) *= divi.at(i); 
        };
        auto differential = [&](fps &f) -> void { //inplaceで微分.
            if(f.size() == 0) return;
            f.erase(f.begin());
            T multi = 0;
            for(int i=0; i<f.size(); i++) f.at(i) *= ++multi;
        };
 
        fps f({1}),g({1}),z1,z2({1,1}); //何やってるか本当に意味わからずコメント書けない 後で確認.
        if((*this).size() > 1) f.push_back((*this).at(1));
        else f.push_back(0);
        for(int m=2; m<deg; m<<=1){
            auto ff = f;
            ff.resize(2*m);
            NTT(ff); z1 = z2;
            fps z(m);
            for(int i=0; i<m; i++) z.at(i) = ff.at(i)*z1.at(i);
            INTT(z);
            for(int i=0; i<m/2; i++) z.at(i) = 0;
            for(int i=m/2; i<m; i++) z.at(i) *= divi.at(m);
            NTT(z);
            for(int i=0; i<m; i++) z.at(i) *= -z1.at(i);
            INTT(z);
            for(int i=m/2; i<m; i++) g.emplace_back(z.at(i)*divi.at(m));
            z2 = g;
            z2.resize(2*m);
            NTT(z2);
            fps h = (*this).prefix(m);
            differential(h);
            h.emplace_back(T(0));
            NTT(h);
            for(int i=0; i<m; i++) h.at(i) *= ff.at(i);
            INTT(h);
            for(int i=0; i<m; i++) h.at(i) *= divi.at(m);
            h -= f.diff();
            h.resize(2*m);
            for(int i=0; i<m-1; i++) h.at(m+i) = h.at(i),h.at(i) = 0;
            NTT(h);
            for(int i=0; i<2*m; i++) h.at(i) *= z2.at(i);
            INTT(h);
            for(int i=0; i<2*m; i++) h.at(i) *= divi.at(2*m);
            h.pop_back();
            integral(h);
            int n = min((int)(*this).size(),2*m);
            for(int i=m; i<n; i++) h.at(i) += (*this).at(i);
            for(int i=0; i<m; i++) h.at(i) = 0;
            NTT(h);
            for(int i=0; i<2*m; i++) h.at(i) *= ff.at(i);
            INTT(h);
            for(int i=0; i<2*m; i++) h.at(i) *= divi.at(2*m);
            for(int i=m; i<2*m; i++) f.emplace_back(h.at(i));
        }
        return f.prefix(deg);
    }
    fps exp2(int deg=-1)const{ //定数重いやつinvと同じ O(nlogn).
        //NTT-friendlyじゃないとK=10^5で1sec以上かかる 畳み込みが遅い.
        assert((*this).size() == 0 || (*this).at(0) == 0);
        if(deg == -1) deg = (*this).size();
        fps ret(1); ret.at(0) = 1;
        for(int i=1; i<deg; i<<=1){
            //ニュートン法 g2m<-gm*(1-log(gm)+f) mod x^2n 再掲.
            ret = (ret*((*this).prefix(2*i)+T(1)-ret.log(2*i,false))).prefix(2*i); //logの引数普段と違う.
        }
        return ret.prefix(deg);
    }
    fps pow(long long K,int deg=-1,bool NTTfriendly = true)const{ //K乗を返すO(nlogn) mod10^9+7で3番目引数false.
        //f^k = exp(klog(f))を使う.
        //logfが計算できるように調整する.
        int n = (*this).size();
        long long mod = mint::getmod();
        if(deg == -1) deg = n;
        if(K == 0){ //0乗はx^0だけ係数1.
            fps ret(deg);
            if(deg > 0) ret.at(0) = 1;
            return ret;
        }
        for(int i=0; i<n; i++){
            if((*this).at(i) != 0){ //0じゃなかったらOK.
                if(NTTfriendly){
                    T div = T(1)/(*this).at(i); //*([x^i]f)^Kと *x^(i*k)の分は後回し.
                    fps ret = ((((*this)*div)>>i).log(deg)*(K%mod)).exp(deg);
                    ret *= T((*this).at(i)).pow(K); //[x^i]f^Kの分.
                    ret = (ret<<(i*K)).prefix(deg); //*x^(i*k)の分.
                    return ret;
                }
                else{
                    T div = T(1)/(*this).at(i); //*([x^i]f)^Kと *x^(i*k)の分は後回し.
                    fps ret = ((((*this)*div)>>i).log(deg,false)*(K%mod)).exp2(deg);
                    ret *= T((*this).at(i)).pow(K); //[x^i]f^Kの分.
                    ret = (ret<<(i*K)).prefix(deg); //*x^(i*k)の分.
                    return ret;
                }
            }
            if(K >= deg || (i+1)*K >= deg) break; //((i+1)*K)乗未満は0確定 int128回避用にK>=deg(degがllはやばい).
        }
        return fps(deg,0); //fの係数全て0なら係数全て0.
    }
 
    fps prefix(int siz)const{ //先頭siz項を返す なかったら0埋め. O(siz).
        fps ret((*this).begin(),(*this).begin()+min((int)(*this).size(),siz));
        if(ret.size() < siz) ret.resize(siz,0);
        return ret;
    }
    void del0(){ //末尾の0を消す O(n).
        while((*this).size() && (*this).back() == 0) (*this).pop_back();
    }
    fps rev()const{ //ひっくり返す O(n).
        fps ret(*this);
        reverse(ret.begin(),ret.end());
        return ret;
    }
    pair<fps,fps> getQR(const fps &b)const{ //多項式の商と余りを同時に得る O(nlogn).
        fps Q = (*this)/b,R = (*this)-Q*b;
        R.del0();
        return {Q,R};
    } 
 
    fps cumulativeNtimes(int N,T b,int deg=-1){ //1/(1-bx)^Nをdeg次まで返す 指定なしはN次まで.
        //負の二項定理を使う. 1/(1-x)^N=Σ[i=0~∞]((n+i-1) choose i)(bx^i);
        //fps{}.cumulativeNtime()で無理やり関数を呼び出す.
        assert(N <= 0); //N=0も駄目? {1}を返すべき所{0}になる.
        if(deg == -1) deg = N+1; 
        long long mod = mint::getmod();
        int Limit = N+deg; //Limit 必要なサイズ fac->x! facinv->1/x! inv->1/x.
        vector<T> FAC(Limit+1,1); for(int i=1; i<=Limit; i++) FAC.at(i) = FAC.at(i-1)*i;
        vector<T> FACinv(Limit+1); FACinv.at(min((int)mod-1,Limit)) = FAC.at(min((int)mod-1,Limit)).inv();
        for(int i=min((int)mod-2,Limit-1); i>=0; i--) FACinv.at(i) = FACinv.at(i+1)*(i+1);
        auto nCr = [&](int n, int r) -> T {
            if(n < r || r < 0 || n < 0) return 0;
            return FAC.at(n)*FACinv.at(r)*FACinv.at(n-r);
        };
        fps ret(deg); T value = 1;
        for(int i=0; i<deg; i++) ret.at(i) = nCr(N+i-1,i)*value,value *= b;
        return ret; 
    }
    fps Taylorshift(long long C)const{ //Σ[i=0~n]Ai*(x+c)^iを返す O(nlogn).
        //Σ[i=0~n]x^i/i! Σ[k=0~n-i](A[i+k]*(i+k)!)*(c^k/k!)になる.
        //kの部分はXi=Ai*i!,Yi=c^i/i!として.Zi=ΣX[i+k]Yk.
        //これは[x^(i+n)]X*rev(Y)で求められる.
        long long mod = mint::getmod();
        mint c = (C%mod+mod)%mod,pc = 1;
        if(c == 0) return (*this);
        int deg = (*this).size(); //deg 必要なサイズ fac->x! facinv->1/x! inv->1/x.
        vector<mint> fac(deg+1,1); for(int i=1; i<=deg; i++) fac.at(i) = fac.at(i-1)*i;
        vector<mint> facinv(deg+1); facinv.at(min((int)mod-1,deg)) = fac.at(min((int)mod-1,deg)).inv();
        for(int i=min((int)mod-2,deg-1); i>=0; i--) facinv.at(i) = facinv.at(i+1)*(i+1);
        
        fps X(deg),Y(deg);
        for(int i=0; i<deg; i++) X.at(i) = (*this).at(i)*fac.at(i),Y.at(deg-1-i) = pc*facinv.at(i),pc *= c;
        X *= Y;
        fps ret(deg);
        for(int i=0; i<deg; i++) ret.at(i) = X.at(i+deg-1)*facinv.at(i);
        return ret;
    }
};
using fps = FormalPowerSeries<mint>;
//mod998244353以外のNTT-friendlyの時は色々気を付ける 後で書き直すかも?.

pair<fps,fps> SumfpsFraction(vector<fps> A,vector<fps> B){ //次数の和=n O(nlog^2n).
    //ΣAi/Biを求める 分割統治でO(nlog^2n).
    //a/b+c/d = (ad+bc)/bd 面倒なのでvector<mint>は用意せずfpsだけ;
    assert(A.size() == B.size() && A.size());
    int n = A.size();
    auto comp = [&](int a,int b) -> bool {return A[a].size()+B[a].size()>A[b].size()+B[b].size();};
    priority_queue<int,vector<int>,decltype(comp)> Q(comp);
    for(int i=0; i<n; i++) Q.push(i);
    while(Q.size() > 1){
        int p = Q.top(); Q.pop();
        int q = Q.top(); Q.pop();
        fps num = A.at(p)*B.at(q)+B.at(p)*A.at(q);
        A.at(p) = num; B.at(p) *= B.at(q);
        Q.push(p);
    }
    int leader = Q.top();
    return {A.at(leader),B.at(leader)};
}

pair<vector<mint>,vector<mint>> SummintFraction(vector<vector<mint>> A,vector<vector<mint>> B){ //次数の和=n O(nlog^2n).
    //ΣAi/Biを求める 分割統治でO(nlog^2n).
    //a/b+c/d = (ad+bc)/bd 面倒なのでvector<mint>は用意せずfpsだけ;
    assert(A.size() == B.size() && A.size());
    int n = A.size();
    auto comp = [&](int a,int b) -> bool {return A[a].size()+B[a].size()>A[b].size()+B[b].size();};
    priority_queue<int,vector<int>,decltype(comp)> Q(comp);
    for(int i=0; i<n; i++) Q.push(i);
    while(Q.size() > 1){
        int p = Q.top(); Q.pop();
        int q = Q.top(); Q.pop();
        vector<mint> num = convolution(A.at(p),B.at(q));
        vector<mint> num2 = convolution(B.at(p),A.at(q));
        if(num.size() < num2.size()) num.resize(num2.size());
        for(int i=0; i<num2.size(); i++) num.at(i) += num2.at(i);
        A.at(p) = num; B.at(p) = convolution(B.at(p),B.at(q));
        Q.push(p);
    }
    int leader = Q.top();
    return {A.at(leader),B.at(leader)};
}


ostream &operator<<(ostream &os,const fps &a){
    for(auto v : a) cout << v.val() << " ";
    return os;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    mint::setmod(998244353);
    int N,S; cin >> N >> S;
    vector<vector<mint>> A(N),B(N);
    mint divS = mint(1)/S;
    for(int i=0; i<N; i++){
        int p; cin >> p;
        mint one = divS*p,two = one*one;
        A.at(i) = {two}; B.at(i) = {1,one};
    }
    auto [n,d] = SummintFraction(A,B);
    mint answer = 0,fac = 1;
    for(int i=0; i<n.size(); i++) answer += n.at(i)*fac*(i+2),fac *= i+2;
    cout << answer.val() << endl;
}