#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

using namespace std;
//--------------------------------------------------------------------
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(n) for(ll _=0;_<(ll)n;++_)
#define rep2(i,n) for(ll i=0;i<(ll)n;++i)
#define rep3(i,a,b) for(ll i=(ll)a;i<(ll)b;++i)
#define rep4(i,a,b,c) for(ll i=(ll)a;i<(ll)b;i+=(ll)c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#ifdef _DEBUG
#define pass(...) __VA_ARGS__ ;

#define debug1(a) cerr<<#a<<": "<<a<<"\n"
#define debug2(a,b) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"

/*
#define debug1(a) cout<<#a<<": "<<a<<"\n"
#define debug2(a,b) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"
*/

#define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__)
#define koko cerr << "koko\n";
#else
#define debug(...) void(0)
#define pass(...) void(0);
#define koko void(0);
#endif
#define mp make_pair
//#define fi first
//#define se second
void myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}
void doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}
using ll = long long;
using ld = long double;
using dou = double;
template<class First,class Second>ostream& operator<<(ostream& os,const pair<First,Second>& pp)
{return os << "{" << pp.first << "," << pp.second << "}";}
template<class T>ostream& operator<<(ostream& os,const vector<T>& VV)
{if(VV.empty())return os<<"[]";os<<"[";rep(i,VV.size())os<<VV[i]<<(i==int(VV.size()-1)?"]":",");return os;}
template<class T>ostream& operator<<(ostream& os,const set<T>& SS)
{if(SS.empty())return os<<"[]";os<<"[";auto ii=SS.begin();for(;ii!=SS.end();ii++)os<<*ii<<(ii==prev(SS.end())?"]":",");return os;}
template<class Key,class Tp>ostream& operator<<(ostream& os,const map<Key,Tp>& MM)
{if(MM.empty())return os<<"[]";os<<"[";auto ii=MM.begin();for(;ii!=MM.end();ii++)os<<"{"<<ii->first<<":"<<ii->second<<"}"<<(ii==prev(MM.end())?"]":",");return os;}
const int inf = 1 << 30;
const ll INF = 1LL << 61;
const ld pi = 3.14159265358;
const ll mod1 = 1000000007LL;
const ll mod2 = 998244353LL;
typedef pair<ll,ll> P;
template<class T, class U> inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T, class U> inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }
ll modpow(ll n,ll m,ll MOD){
    if(m == 0)return 1;
    if(m < 0)return 0;
    ll res = 1;
    n %= MOD;
    while(m){
        if(m & 1)res = (res * n) % MOD;
        m >>= 1;
        n *= n;
        n %= MOD;
    }
    return res;
}
ll mypow(ll n,ll m){
    if(m == 0)return 1;
    if(m < 0)return -1;
    ll res = 1;
    while(m){
        if(m & 1)res = (res * n);
        m >>= 1;
        n *= n;
    }
    return res;
}

inline bool isp(ll n){
    bool res = true;
    if(n == 1 || n == 0)return false;
    else{
        for(ll i = 2;i * i <= n;i++){
            if(n % i == 0){
                res = false;
                break;
            }
        }
        return res;
    }
}
inline bool Yes(bool b = 1){cout << (b ? "Yes\n":"No\n");return b;}
inline bool YES(bool b = 1){cout << (b ? "YES\n":"NO\n");return b;}
map<ll,ll> primefactor(ll n){
    map<ll,ll> ma;
    if(n <= 1)return ma;
    ll m = n;
    for(ll i = 2;i * i <= n;i++){
        while(m % i == 0){
            ma[i]++;
            m /= i;
        }
    }
    if(m != 1)ma[m]++;
    return ma;
}
vector<ll> divisor(ll n,bool sorted = true,bool samein = false){
    vector<ll> res;
    for(ll i = 1;i * i <= n;i++){
        if(n % i == 0){
            res.push_back(i);
            if(i * i != n || samein)res.push_back(n / i);
        }
    }
    if(sorted)sort(all(res));
    return res;
}

ll __lcm(ll a,ll b){return a / __gcd(a,b) * b;}

template<class T>T sum(const vector<T> &V){T r=0;for(auto x:V)r+=x;return r;}
template<class T>T sum(const initializer_list<T> &V){T r=0;for(auto x:V)r+=x;return r;}


//#include <atcoder/all>
//#include "atcoder/lazysegtree.hpp"
//using namespace atcoder;


//--------------------------------------------------------------------














long long extgcd(long long a,long long b,long long &x,long long &y){
    if(b == 0){
        x = 1;
        y = 0;
        return a;
    }
    long long d = extgcd(b,a % b,y,x);
    y -= a / b * x;
    return d;
}

long long modinv(long long a,long long p){
    long long b = p, u = 1, v = 0;
    while(b){
        long long t = a / b;
        a -= t * b;std::swap(a, b);
        u -= t * v;std::swap(u, v);
    }
    u %= p;
    if(u < 0)u += p;
    return u;
}



/**
 * @brief garner precalc
 * @return long long 
 */
long long pregarner(std::vector<long long> &rems,std::vector<long long> &mods,long long MOD){
    assert(rems.size() == mods.size());
    for(int i = 0;i < int(rems.size());i++){
        for(int j = 0;j < i;j++){
            long long g = std::gcd(mods[i],mods[j]);
            if((rems[i] - rems[j]) % g != 0)return -1;
            mods[i] /= g;mods[j] /= g;
            long long gi = std::gcd(g,mods[i]),gj = g / gi;
            do{
                g = std::gcd(gi,gj);
                gi *= g;gj /= g;
            }while(g != 1);
            mods[i] *= gi;mods[j] *= gj;
            rems[i] %= mods[i];rems[j] %= mods[j];
        }
    }
    long long res = 1;
    for(long long &a : mods)res = res * a % MOD;
    return res;
}

/**
 * @brief returns a integer where rems[i](mod.mods[i]).
 * @return long long 
 */
long long garner(std::vector<long long> rems,std::vector<long long> mods,long long MOD){
    assert(rems.size() == mods.size());
    mods.push_back(MOD);
    int sz = mods.size();
    std::vector<long long> cof(sz,1LL),con(sz,0LL);
    for(int i = 0;i < sz - 1;i++){
        long long cur = (rems[i] - con[i]) * modinv(cof[i],mods[i]) % mods[i];
        if(cur < 0)cur += mods[i];
        for(int j = i + 1;j < sz;j++){
            con[j] = (con[j] + cur * cof[j]) % mods[j];
            cof[j] = cof[j] * mods[i] % mods[j];
        }
    }
    return con.back();
}










template<long long MOD = 1000000007>
struct modint {
    using mint = modint<MOD>;
    long long x;
    modint(long long a = 0):x((a % MOD + MOD) % MOD){}
    inline constexpr modint operator-()const noexcept{return modint(-x);}
    inline constexpr modint &operator+=(const modint &a)noexcept{
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    inline constexpr modint &operator-=(const modint &a)noexcept{
        if ((x -= a.x) < 0) x += MOD;
        return *this;
    }
    inline constexpr modint &operator*=(const modint &a)noexcept{
        (x *= a.x) %= MOD;
        return *this;
    }
    inline constexpr modint &operator++()noexcept{
        x++;
        if(x == MOD)x = 0;
        return *this;
    }
    inline constexpr modint operator++(int)noexcept{
        modint res(*this);
        operator++();
        return res;
    }
    inline constexpr modint &operator--()noexcept{
        x--;
        if(x == -1)x = MOD - 1;
        return *this;
    }
    inline constexpr modint operator--(int)noexcept{
        modint res(*this);
        operator--();
        return res;
    }
    inline constexpr modint operator+(const modint &a)const noexcept{
        modint res(*this);
        return res += a;
    }
    inline constexpr modint operator-(const modint &a)const noexcept{
        modint res(*this);
        return res -= a;
    }
    inline constexpr modint operator*(const modint &a)const noexcept{
        modint res(*this);
        return res *= a;
    }
    inline constexpr modint inv()const{
        long long a = x,b = MOD,u = 1,v = 0;
        while(b){
            long long t = a / b;
            a -= t * b;std::swap(a,b);
            u -= t * v;std::swap(u,v);
        }
        return u;
    }
    inline constexpr modint &operator/=(const modint &a)noexcept{return (*this) *= a.inv();}
    inline constexpr modint operator/(const modint &a)const noexcept{
        modint res(*this);
        return res /= a;
    }
    inline constexpr bool operator==(const modint &a)const noexcept{return x == a.x;}
    friend std::istream &operator>>(std::istream &is,modint &a) {
        is >> a.x;
        a.x = (a.x % MOD + MOD) % MOD;
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os,const modint &a){
        os << a.x;
        return os;
    }
    long long getmod(){return MOD;}
    friend mint modpow(mint a,long long b)noexcept{
        mint res(1);
        while(b){
            if(b & 1)res *= a;
            a *= a;
            b >>= 1;
        }
        return res;
    }
};
//using mint = modint<1'000'000'007>::mint;




//ex. (2013265921,137,27),(998244353,31,23),(469762049,30,26)
template<long long MOD,int base,int max_exp>
struct NTT_primitive{
    using mint = modint<MOD>;
    std::vector<mint> bases,invs;
    NTT_primitive(){
        bases.resize(max_exp + 1);invs.resize(max_exp + 1);
        bases[max_exp] = base;
        invs[max_exp] = mint(base).inv();
        for(int i = max_exp - 1;i >= 0;i--){
            bases[i] = bases[i + 1] * bases[i + 1];
            invs[i] = invs[i + 1] * invs[i + 1];
        }
    }
    void dft(std::vector<mint>& vec,int t){
        int sz = vec.size();
        if(sz == 1)return;
        std::vector<mint> veca,vecb;
        for(int i = 0;i < sz / 2;i++){
            veca.push_back(vec[i * 2]);
            vecb.push_back(vec[i * 2 + 1]);
        }
        dft(veca,t);
        dft(vecb,t);
        
        int e = __builtin_ffsll(sz) - 1;
        mint now = 1,zeta = (t == 1 ? bases[e]:invs[e]);
        for(int i = 0;i < sz;i++){
            vec[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];
            now *= zeta;
        }
    }
    std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
        // assert(A.size() == B.size());
        int sz = 1;
        while(sz < int(A.size() + B.size()))sz <<= 1;
        std::vector<mint> f(sz),g(sz);
        for(int i = 0;i < int(A.size());i++)f[i] = A[i];
        for(int i = 0;i < int(B.size());i++)g[i] = B[i];
        dft(f,1);dft(g,1);
        for(int i = 0;i < sz;i++)f[i] = f[i] * g[i];
        dft(f,-1);
        mint inv = mint(sz).inv();
        for(int i = 0;i < sz;i++)f[i] *= inv;
        return f;
    }
    void dft(std::vector<long long>& vec,int t){
        int sz = vec.size();
        if(sz == 1)return;
        std::vector<long long> veca,vecb;
        for(int i = 0;i < sz / 2;i++){
            veca.push_back(vec[i * 2]);
            vecb.push_back(vec[i * 2 + 1]);
        }
        dft(veca,t);
        dft(vecb,t);
        
        int e = __builtin_ffsll(sz) - 1;
        long long now = 1,zeta = (t == 1 ? bases[e].x:invs[e].x);
        for(int i = 0;i < sz;i++){
            vec[i] = (veca[i % (sz / 2)] + now * vecb[i % (sz / 2)] % MOD) % MOD;
            now = now * zeta % MOD;
        }
    }
    std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
        // assert(A.size() == B.size());
        int sz = 1;
        while(sz < int(A.size() + B.size()))sz <<= 1;
        std::vector<long long> f(sz),g(sz);
        for(int i = 0;i < int(A.size());i++)f[i] = A[i] % MOD;
        for(int i = 0;i < int(B.size());i++)g[i] = B[i] % MOD;
        dft(f,1);dft(g,1);
        for(int i = 0;i < sz;i++)f[i] = f[i] * g[i] % MOD;
        dft(f,-1);
        long long inv = modinv(sz,MOD);
        for(int i = 0;i < sz;i++)f[i] = f[i] * inv % MOD;
        return f;
    }
};





template<long long MOD>
struct NTT_all{
    NTT_primitive<2013265921,137,27> ntt1;
    NTT_primitive<998244353,31,23> ntt2;
    NTT_primitive<469762049,30,26> ntt3;
    using mint = modint<MOD>;
    using mint1 = modint<2013265921>;
    using mint2 = modint<998244353>;
    using mint3 = modint<469762049>;
    NTT_all(){}
    
    std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
        int sza = A.size(),szb = B.size();
        std::vector<mint1> A1(sza),B1(szb);
        std::vector<mint2> A2(sza),B2(szb);
        std::vector<mint3> A3(sza),B3(szb);
        for(int i = 0;i < sza;i++){
            A1[i] = A[i].x;A2[i] = A[i].x;A3[i] = A[i].x;
        }
        for(int i = 0;i < szb;i++){
            B1[i] = B[i].x;B2[i] = B[i].x;B3[i] = B[i].x;
        }
        auto C1 = ntt1.convolution(A1,B1);
        auto C2 = ntt2.convolution(A2,B2);
        auto C3 = ntt3.convolution(A3,B3);
        int rs = C1.size();
        std::vector<mint> res(rs);
        for(int i = 0;i < rs;i++){
            std::vector<long long> r = {C1[i].x,C2[i].x,C3[i].x},m = {2013265921,998244353,469762049};
            res[i] = garner(r,m,MOD);
        }
        return res;
    }
    std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
        int sza = A.size(),szb = B.size();
        std::vector<long long> A1(sza),B1(szb),A2(sza),B2(szb),A3(sza),B3(szb);
        for(int i = 0;i < sza;i++){
            A1[i] = A[i] % 2013265921;
            A2[i] = A[i] % 998244353;
            A3[i] = A[i] % 469762049;
        }
        for(int i = 0;i < szb;i++){
            B1[i] = B[i] % 2013265921;
            B2[i] = B[i] % 998244353;
            B3[i] = B[i] % 469762049;
        }
        auto C1 = ntt1.convolution(A1,B1);
        auto C2 = ntt2.convolution(A2,B2);
        auto C3 = ntt3.convolution(A3,B3);
        int rs = C1.size();
        std::vector<long long> res(rs);
        for(int i = 0;i < rs;i++){
            std::vector<long long> r = {C1[i],C2[i],C3[i]},m = {2013265921,998244353,469762049};
            res[i] = garner(r,m,MOD) % MOD;
        }
        return res;
    }
};






namespace bigint_convolution{
    bool is_set = false;
    std::function<std::vector<long long>(std::vector<long long>,std::vector<long long>)> f;
    void set(const std::function<std::vector<long long>(std::vector<long long>,std::vector<long long>)>& _f){
        is_set = true;
        f = _f;
    }
    std::vector<long long> convolution(const std::vector<long long>& a,const std::vector<long long>& b){
        assert(is_set);
        return f(a,b);
    }
    std::vector<long long> naive(const std::vector<long long>& a,const std::vector<long long>& b){
        int n = int(a.size()),m = int(b.size());
        std::vector<long long> res(n + m - 1);
        if(n < m)
            for(int j = 0;j < m;j++)for(int i = 0;i < n;i++)res[i + j] += a[i] * b[j];
        else
            for(int i = 0;i < n;i++)for(int j = 0;j < m;j++)res[i + j] += a[i] * b[j];
        return res;
    };
};

template<int d,int base>
struct bigint{
    using bint = bigint<d,base>;
    bigint(const std::string& _s){
        sign = 1;
        dat.clear();
        if(_s.empty())return;
        if(_s[0] == '-')sign = -1;
        std::string s = sign == 1 ? _s : _s.substr(1);
        int i;
        for(i = int(s.size()) - d;i >= 0;i -= d){
            assert('0' <= s[i] && s[i] <= '9');
            dat.push_back(std::stoll(s.substr(i,d)));
        }
        if(i + d)dat.push_back(std::stoll(s.substr(0,i + d)));
        while(!dat.empty() && dat.back() == 0)dat.pop_back();
    }
    bigint(long long n = 0){
        sign = 1;
        dat.clear();
        if(n < 0)sign = -1,n = -n;
        while(n){
            dat.push_back(n % base);
            n /= base;
        }
    }
    int size()const{return int(dat.size());}
    int number_len()const{
        if(size() == 0)return 0;
        int res = (int(dat.size()) - 1) * d;
        int b = 1,p = 0;
        while(b <= dat.back())p++,b *= 10;
        return res + p;
    }
    std::string to_string()const{
        if(size() == 0)return "0";
        std::string res = "";
        if(sign == -1)res = "-";
        auto to_string_pad = [](long long m,int _d){
            std::string r = std::to_string(m);
            std::string ap(_d - int(r.size()),'0');
            return ap + r;
        };
        for(int i = size() - 1;i >= 0;i--){
            if(i != size() - 1)res += to_string_pad(dat[i],d);
            else res += std::to_string(dat[i]);
        }
        return res;
    }
    long long to_ll()const{
        long long res = 0;
        for(int i = size() - 1;i >= 0;i--)res = res * base + dat[i];
        return sign * res;
    }
    void norm(){
        if(dat.empty())return;
        for(int i = 0;i < size() - 1;i++){
            long long nex = dat[i] / base;
            if(nex * base > dat[i])nex--;
            dat[i] -= nex * base;
            dat[i + 1] += nex;
        }
        while(dat.back() >= base){
            long long nex = dat.back() / base;
            dat.back() -= nex * base;
            dat.push_back(nex);
        }
        while(!dat.empty() && dat.back() == 0)dat.pop_back();
    }

    inline constexpr bool operator<(const bint& a)const noexcept{
        if(a.dat.empty())return false;
        else if(sign != a.sign)return sign < a.sign;
        else if(sign == -1)return (-a) < (-bint(*this));
        else if(number_len() != a.number_len())return number_len() < a.number_len();
        else{
            for(int i = size() - 1;i >= 0;i--)if(dat[i] != a.dat[i])return dat[i] < a.dat[i];
            return false;
        }
    }
    inline constexpr bool operator>(const bint& a)const noexcept{return a < bint(*this);}
    inline constexpr bool operator<=(const bint& a)const noexcept{return !(a < bint(*this));}
    inline constexpr bool operator>=(const bint& a)const noexcept{return !(bint(*this) < a);}
    inline constexpr bool operator==(const bint& a)const noexcept{return dat == a.dat;}
    inline constexpr bool operator!=(const bint& a)const noexcept{return dat != a.dat;}

    inline constexpr bint operator-()const noexcept{
        bint res(*this);
        res.sign = -res.sign;
        return res;
    }
    friend bint abs(const bint& a){return a.sign == -1 ? -a : a;}

    inline constexpr bint &operator+=(const bint& a)noexcept{
        if(sign != a.sign)return *this -= (-a);
        else{
            if(size() < a.size())dat.resize(a.size());
            for(int i = 0;i < a.size();i++)dat[i] += a.dat[i];
            norm();
            return *this;
        }
    }
    inline constexpr bint &operator-=(const bint& a)noexcept{
        if(sign != a.sign)return *this += (-a);
        else if(abs(bint(*this)) < abs(a)){
            *this = a - *this;sign = -sign;
            return *this;
        }
        else{
            for(int i = 0;i < a.size();i++)dat[i] -= a.dat[i];
            norm();
            return *this;
        }
    }

    inline constexpr bint &operator++()noexcept{return *this += bint(1);}
    inline constexpr bint operator++(int)noexcept{operator++();return bint(*this);}
    inline constexpr bint &operator--()noexcept{return *this -= bint(1);}
    inline constexpr bint operator--(int)noexcept{operator--();return bint(*this);}

    inline constexpr bint &operator*=(const bint& a)noexcept{
        if(size() == 0 || a.size() == 0)return *this = bint(0);
        if(std::min(size(),a.size()) <= 60)dat = bigint_convolution::naive(dat,a.dat);
        else dat = bigint_convolution::convolution(dat,a.dat);
        norm();
        sign *= a.sign;
        return *this;
    }
    inline constexpr bint mul2()const noexcept{
        bint res(*this);
        for(auto& x : res.dat)x *= 2;
        res.norm();
        return res;
    }
    inline constexpr bint div2()const noexcept{
        bint res(*this);
        int nex = 0;
        for(int i = res.size() - 1;i >= 0;i--){
            long long cur = (res.dat[i] + nex * base);
            res.dat[i] = cur >> 1;
            nex = cur & 1;
        }
        while(!res.dat.empty() && res.dat.back() == 0)res.dat.pop_back();
        return res;
    }
    inline constexpr int rem2()const noexcept{
        if(dat.empty())return 0;
        else return dat[0] & 1;
    }
    inline constexpr bint &operator>>=(int k)noexcept{
        dat = std::vector<long long>(dat.begin() + std::min(k,int(size())),dat.end());
        return *this;
    }
    inline constexpr bint &operator<<=(int k)noexcept{
        if(!dat.empty()){
            std::vector<long long> add(k,0);
            dat.insert(dat.begin(),add.begin(),add.end());
        }
        return *this;
    }

    inline constexpr bint &operator/=(long long v)noexcept{
        if(v < 0)sign = -sign,v = -v;
        for(int i = size() - 1,rem = 0;i >= 0;i--){
            long long cur = dat[i] + rem * (long long)(base);
            dat[i] = (long long)(cur / v);
            rem = (long long)(cur % v);
        }
        norm();
        return *this;
    }
    friend std::pair<bint,bint> divmod_naive(const bint& _a,const bint& _b){
        bint zero,s,t;
        bint a = abs(_a),b = abs(_b);
        if(a < b)return std::make_pair(zero,a);
        bint ar = b;
        s.dat.resize(a.size()),t.dat.resize(b.size());
        int tx = a.size() - 1;
        for(;tx >= 0;--tx)if(a.dat[tx] > 0)break;
        for(int i = tx; i >= 0; --i){
            t <<= 1;
            t += a.dat[i];
            long long lo = 0,hi = base;
            if(t >= ar){
                while(hi - lo > 1){
                    int mid = (hi + lo) / 2;
                    if(ar * mid > t)hi = mid;
                    else lo = mid;
                }
                t -= ar * lo;
            }
            s.dat[i] = lo;
        }
        if(_a.sign == _b.sign)s.sign = 1,t.sign = 1;
        else s.sign = -1,t.sign = 1;
        s.norm();t.norm();
        return std::make_pair(s,t);
    }
    inline constexpr bint &operator/=(const bint& a)noexcept{
        if(size() - a.size() <= 10)return *this = divmod_naive(bint(*this),a).first;
        else return *this = this->div_fast(a);
    }
    
    inline constexpr bint &operator%=(const bint& a)noexcept{
        if(size() - a.size() <= 10)return *this = divmod_naive(bint(*this),a).second;
        else return *this = bint(*this) - this->div_fast(a) * a;
    }

    inline constexpr bint operator+(const bint& a)const noexcept{return bint(*this) += a;}
    inline constexpr bint operator-(const bint& a)const noexcept{return bint(*this) -= a;}
    inline constexpr bint operator*(const bint& a)const noexcept{return bint(*this) *= a;}
    inline constexpr bint operator>>(int k)const noexcept{return bint(*this) >>= k;}
    inline constexpr bint operator<<(int k)const noexcept{return bint(*this) <<= k;}
    inline constexpr bint operator/(long long v)const noexcept{return bint(*this) /= v;}
    inline constexpr bint operator/(const bint& a)const noexcept{return bint(*this) /= a;}
    inline constexpr bint operator%(const bint& a)const noexcept{return bint(*this) %= a;}

    friend std::ostream &operator<<(std::ostream& os,const bint& a){return os << a.to_string();}
    friend std::istream &operator>>(std::istream& is,bint& a){
        std::string s;
        is >> s;
        a = bint(s);
        return is;
    }

    explicit operator bool()const noexcept{return !dat.empty();}
    explicit operator int()const noexcept{return to_ll();}
    using long_long = long long;
    explicit operator long_long()const noexcept{return to_ll();}


    int sign;
    std::vector<long long> dat;
    bint div_fast(const bint& _a)const noexcept{
        bint a = abs(*this),b = abs(_a);
        if(a < b)return bint();
        int tar = a.size() - b.size() + 1,m = 1;
        while(b.dat.back() * m * 10 < base)m *= 10;
        bint inv(m * base),pre(0);
        const bint two(2);
        while(inv != pre){
            pre = inv;
            inv *= (two << 2) - inv * b.dat.back();
            inv >>= 2;
        }
        int cur = 2,bcur = 1;
        pre = bint(0);
        while(inv != pre){
            bint c;
            c.dat = std::vector<long long>(b.dat.end() - bcur,b.dat.end());
            pre = inv;
            inv *= (two << (cur + bcur - 1)) - inv * c;
            int nex = std::min(cur << 1,tar);
            inv.dat = std::vector<long long>(inv.dat.end() - nex,inv.dat.end());
            cur = nex;
            bcur = std::min(bcur << 1,b.size());
        }
        inv.dat = std::vector<long long>(inv.dat.end() - tar,inv.dat.end());
        bint res = a * inv;res.dat = std::vector<long long>(res.dat.begin() + a.size(),res.dat.end());
        bint mul = res * b;
        while(mul + b <= a){
            res++;
            mul += b;
        }
        res.sign = sign * _a.sign;
        return res;
    }
};
using bint = bigint<4,10000>;





#include <type_traits>




#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder






#ifdef _MSC_VER
#include <intrin.h>
#endif





#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder






namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder



namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder



namespace atcoder {

namespace internal {

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }

    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a, const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return std::move(a);
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a, const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }

    return c;
}

}  // namespace atcoder




int main(){
    myset();
    bigint_convolution::set(atcoder::convolution_ll);
    bint _n,m;
    cin >> _n >> m;
    ll n = (_n % 10).to_ll(),ans = 1;
    debug(n,ans);
    while(m){
        if(m.rem2())ans = ans * n % 10;
        n = (n * n) % 10;
        m = m.div2();
    }
    cout << ans << "\n";
}