#include <bits/stdc++.h>
using namespace std;
//#include<atcoder/math>
//using namespace atcoder;
using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
constexpr ll MAX = 2000000000000000000;
constexpr ld PI = 3.14159265358979;
constexpr ll MOD = 998244353;//2024948111;
ld dotorad(ld K){ return PI * K / 180.0; }
ld radtodo(ld K){ return K * 180.0 / PI; }
mt19937 mt;
void randinit(){ srand((unsigned)time(NULL));mt = mt19937(rand()); }
ll modpow(ll A,ll B,ll M){
    ll r = 1,p = A;
    while(B > 0){
        if(B % 2 == 1) r = (r * p) % M;
        p = (p * p) % M;
        B /= 2;
    }
    return r;
}
vector<ll> fac,finv,inv;
void COMinit(ll n = 1000000){
    fac.resize(n);
    finv.resize(n);
    inv.resize(n);
    inv[1] = 1;
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    ll i;
    for(i = 2;i < n;i++){
        fac[i] = (fac[i - 1] * i) % MOD;
        inv[i] = MOD - ((inv[MOD % i] * (MOD / i)) % MOD);
        finv[i] = (finv[i - 1] * inv[i]) % MOD;
    }
}
ll COM(ll n,ll m){
    //nCm
    if(n < m) return 0;
    if(n < 0 || m < 0) return 0;
    return (fac[n] * (finv[m] * finv[n - m] % MOD)) % MOD;
}
ll f(ll a,ll b){
    return COM(a + b,a);
}


// https://judge.yosupo.jp/submission/17797

#pragma region kyopro_template
#define Nyaan_template
#include <immintrin.h>
#include <bits/stdc++.h>
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define each(x, v) for (auto &x : v)
#define all(v) (v).begin(), (v).end()
#define sz(v) ((int)(v).size())
#define mem(a, val) memset(a, val, sizeof(a))
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define inc(...)    \
  char __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define die(...)      \
  do {                \
    out(__VA_ARGS__); \
    return;           \
  } while (0)
using namespace std;
using ll = long long;
template <class T>
using V = vector<T>;
using vi = vector<int>;
using vl = vector<long long>;
using vvi = vector<vector<int>>;
using vd = V<double>;
using vs = V<string>;
using vvl = vector<vector<long long>>;
using P = pair<long long,long long>;
using vp = vector<P>;
using pii = pair<int,int>;
using vpi = vector<pair<int,int>>;
constexpr int inf = 1001001001;
constexpr long long infLL = (1LL << 61) - 1;
template <typename T,typename U>
inline bool amin(T &x,U y) {
    return (y < x) ? (x = y,true) : false;
}
template <typename T,typename U>
inline bool amax(T &x,U y) {
    return (x < y) ? (x = y,true) : false;
}
template <typename T,typename U>
ostream &operator<<(ostream &os,const pair<T,U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <typename T,typename U>
istream &operator>>(istream &is,pair<T,U> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os,const vector<T> &v) {
    int s = (int)v.size();
    for(int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is,vector<T> &v) {
    for(auto &x : v) is >> x;
    return is;
}
void in() {}
template <typename T,class... U>
void in(T &t,U &... u) {
    cin >> t;
    in(u...);
}
void out() { cout << "\n"; }
template <typename T,class... U>
void out(const T &t,const U &... u) {
    cout << t;
    if(sizeof...(u)) cout << " ";
    out(u...);
}

#ifdef NyaanDebug
#define trc(...)                   \
  do {                             \
    cerr << #__VA_ARGS__ << " = "; \
    dbg_out(__VA_ARGS__);          \
  } while (0)
#define trca(v, N)       \
  do {                   \
    cerr << #v << " = "; \
    array_out(v, N);     \
  } while (0)
#define trcc(v)                             \
  do {                                      \
    cerr << #v << " = {";                   \
    each(x, v) { cerr << " " << x << ","; } \
    cerr << "}" << endl;                    \
  } while (0)
template <typename T>
void _cout(const T &c) {
    cerr << c;
}
void _cout(const int &c) {
    if(c == 1001001001)
        cerr << "inf";
    else if(c == -1001001001)
        cerr << "-inf";
    else
        cerr << c;
}
void _cout(const unsigned int &c) {
    if(c == 1001001001)
        cerr << "inf";
    else
        cerr << c;
}
void _cout(const long long &c) {
    if(c == 1001001001 || c == (1LL << 61) - 1)
        cerr << "inf";
    else if(c == -1001001001 || c == -((1LL << 61) - 1))
        cerr << "-inf";
    else
        cerr << c;
}
void _cout(const unsigned long long &c) {
    if(c == 1001001001 || c == (1LL << 61) - 1)
        cerr << "inf";
    else
        cerr << c;
}
template <typename T,typename U>
void _cout(const pair<T,U> &p) {
    cerr << "{ ";
    _cout(p.fi);
    cerr << ", ";
    _cout(p.se);
    cerr << " } ";
}
template <typename T>
void _cout(const vector<T> &v) {
    int s = v.size();
    cerr << "{ ";
    for(int i = 0; i < s; i++) {
        cerr << (i ? ", " : "");
        _cout(v[i]);
    }
    cerr << " } ";
}
template <typename T>
void _cout(const vector<vector<T>> &v) {
    cerr << "[ ";
    for(const auto &x : v) {
        cerr << endl;
        _cout(x);
        cerr << ", ";
    }
    cerr << endl << " ] ";
}
void dbg_out() { cerr << endl; }
template <typename T,class... U>
void dbg_out(const T &t,const U &... u) {
    _cout(t);
    if(sizeof...(u)) cerr << ", ";
    dbg_out(u...);
}
template <typename T>
void array_out(const T &v,int s) {
    cerr << "{ ";
    for(int i = 0; i < s; i++) {
        cerr << (i ? ", " : "");
        _cout(v[i]);
    }
    cerr << " } " << endl;
}
template <typename T>
void array_out(const T &v,int H,int W) {
    cerr << "[ ";
    for(int i = 0; i < H; i++) {
        cerr << (i ? ", " : "");
        array_out(v[i],W);
    }
    cerr << " ] " << endl;
}
#else
#define trc(...)
#define trca(...)
#define trcc(...)
#endif

inline int popcnt(unsigned long long a) { return __builtin_popcountll(a); }
inline int lsb(unsigned long long a) { return __builtin_ctzll(a); }
inline int msb(unsigned long long a) { return 63 - __builtin_clzll(a); }
template <typename T>
inline int getbit(T a,int i) {
    return (a >> i) & 1;
}
template <typename T>
inline void setbit(T &a,int i) {
    a |= (1LL << i);
}
template <typename T>
inline void delbit(T &a,int i) {
    a &= ~(1LL << i);
}
template <typename T>
int lb(const vector<T> &v,const T &a) {
    return lower_bound(begin(v),end(v),a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v,const T &a) {
    return upper_bound(begin(v),end(v),a) - begin(v);
}
template <typename T>
int btw(T a,T x,T b) {
    return a <= x && x < b;
}
template <typename T,typename U>
T ceil(T a,U b) {
    return (a + b - 1) / b;
}
constexpr long long TEN(int n) {
    long long ret = 1,x = 10;
    while(n) {
        if(n & 1) ret *= x;
        x *= x;
        n >>= 1;
    }
    return ret;
}
template <typename T>
vector<T> mkrui(const vector<T> &v) {
    vector<T> ret(v.size() + 1);
    for(int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
    return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
    vector<T> ret(v);
    sort(ret.begin(),ret.end());
    ret.erase(unique(ret.begin(),ret.end()),ret.end());
    return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
    vector<int> ord(N);
    iota(begin(ord),end(ord),0);
    sort(begin(ord),end(ord),f);
    return ord;
}
template <typename T = int>
vector<T> mkiota(int N) {
    vector<T> ret(N);
    iota(begin(ret),end(ret),0);
    return ret;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
    vector<int> inv(v.size());
    for(int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
    return inv;
}

struct IoSetupNya {
    IoSetupNya() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetupnya;


#pragma endregion
using namespace std;

using namespace std;

using namespace std;

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
my128_mullo_epu32(const __m128i &a,const __m128i &b) {
    return _mm_mullo_epi32(a,b);
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
my128_mulhi_epu32(const __m128i &a,const __m128i &b) {
    __m128i a13 = _mm_shuffle_epi32(a,0xF5);
    __m128i b13 = _mm_shuffle_epi32(b,0xF5);
    __m128i prod02 = _mm_mul_epu32(a,b);
    __m128i prod13 = _mm_mul_epu32(a13,b13);
    __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02,prod13),
        _mm_unpackhi_epi32(prod02,prod13));
    return prod;
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_mul_128(const __m128i &a,const __m128i &b,const __m128i &r,
    const __m128i &m1) {
    return _mm_sub_epi32(
        _mm_add_epi32(my128_mulhi_epu32(a,b),m1),
        my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a,b),r),m1));
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_add_128(const __m128i &a,const __m128i &b,const __m128i &m2,
    const __m128i &m0) {
    __m128i ret = _mm_sub_epi32(_mm_add_epi32(a,b),m2);
    return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0,ret),m2),ret);
}

__attribute__((target("sse4.2"))) __attribute__((always_inline)) __m128i
montgomery_sub_128(const __m128i &a,const __m128i &b,const __m128i &m2,
    const __m128i &m0) {
    __m128i ret = _mm_sub_epi32(a,b);
    return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0,ret),m2),ret);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
my256_mullo_epu32(const __m256i &a,const __m256i &b) {
    return _mm256_mullo_epi32(a,b);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
my256_mulhi_epu32(const __m256i &a,const __m256i &b) {
    __m256i a13 = _mm256_shuffle_epi32(a,0xF5);
    __m256i b13 = _mm256_shuffle_epi32(b,0xF5);
    __m256i prod02 = _mm256_mul_epu32(a,b);
    __m256i prod13 = _mm256_mul_epu32(a13,b13);
    __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02,prod13),
        _mm256_unpackhi_epi32(prod02,prod13));
    return prod;
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_mul_256(const __m256i &a,const __m256i &b,const __m256i &r,
    const __m256i &m1) {
    return _mm256_sub_epi32(
        _mm256_add_epi32(my256_mulhi_epu32(a,b),m1),
        my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a,b),r),m1));
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_add_256(const __m256i &a,const __m256i &b,const __m256i &m2,
    const __m256i &m0) {
    __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a,b),m2);
    return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0,ret),m2),
        ret);
}

__attribute__((target("avx2"))) __attribute__((always_inline)) __m256i
montgomery_sub_256(const __m256i &a,const __m256i &b,const __m256i &m2,
    const __m256i &m0) {
    __m256i ret = _mm256_sub_epi32(a,b);
    return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0,ret),m2),
        ret);
}
constexpr int SZ = 1 << 19;
uint32_t buf1_[SZ * 2] __attribute__((aligned(64)));
uint32_t buf2_[SZ * 2] __attribute__((aligned(64)));

template <typename mint>
struct NTT {
    static constexpr uint32_t get_pr() {
        uint32_t mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = mod - 1;
        for(u64 i = 2; i * i <= m; ++i) {
            if(m % i == 0) {
                ds[idx++] = i;
                while(m % i == 0) m /= i;
            }
        }
        if(m != 1) ds[idx++] = m;

        uint32_t pr = 2;
        while(1) {
            int flg = 1;
            for(int i = 0; i < idx; ++i) {
                u64 a = pr,b = (mod - 1) / ds[i],r = 1;
                while(b) {
                    if(b & 1) r = r * a % mod;
                    a = a * a % mod;
                    b >>= 1;
                }
                if(r == 1) {
                    flg = 0;
                    break;
                }
            }
            if(flg == 1) break;
            ++pr;
        }
        return pr;
    };

    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level],dy[level];
    mint *buf1,*buf2;

    constexpr NTT() {
        setwy(level);
        buf1 = reinterpret_cast<mint *>(::buf1_);
        buf2 = reinterpret_cast<mint *>(::buf2_);
    }

    constexpr void setwy(int k) {
        mint w[level],y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for(int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1],y[i] = y[i + 1] * y[i + 1];
        dw[0] = dy[0] = w[1] * w[1];
        dw[1] = w[1],dy[1] = y[1],dw[2] = w[2],dy[2] = y[2];
        for(int i = 3; i < k; ++i) {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }

    __attribute__((target("avx2"))) void ntt(mint *a,int n) {
        int k = n ? __builtin_ctz(n) : 0;
        if(k == 0) return;
        if(k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if(k & 1) {
            int v = 1 << (k - 1);
            if(v < 8) {
                for(int j = 0; j < v; ++j) {
                    mint ajv = a[j + v];
                    a[j + v] = a[j] - ajv;
                    a[j] += ajv;
                }
            }
            else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                int j0 = 0;
                int j1 = v;
                for(; j0 < v; j0 += 8,j1 += 8) {
                    __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                    __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                    __m256i naj = montgomery_add_256(T0,T1,m2,m0);
                    __m256i najv = montgomery_sub_256(T0,T1,m2,m0);
                    _mm256_storeu_si256((__m256i *)(a + j0),naj);
                    _mm256_storeu_si256((__m256i *)(a + j1),najv);
                }
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while(v) {
            if(v == 1) {
                mint ww = one,xx = one,wx = one;
                for(int jh = 0; jh < u;) {
                    ww = xx * xx,wx = ww * xx;
                    mint t0 = a[jh + 0],t1 = a[jh + 1] * xx;
                    mint t2 = a[jh + 2] * ww,t3 = a[jh + 3] * wx;
                    mint t0p2 = t0 + t2,t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2,t1m3 = (t1 - t3) * imag;
                    a[jh + 0] = t0p2 + t1p3,a[jh + 1] = t0p2 - t1p3;
                    a[jh + 2] = t0m2 + t1m3,a[jh + 3] = t0m2 - t1m3;
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            }
            else if(v == 4) {
                const __m128i m0 = _mm_set1_epi32(0);
                const __m128i m1 = _mm_set1_epi32(mod);
                const __m128i m2 = _mm_set1_epi32(mod + mod);
                const __m128i r = _mm_set1_epi32(mint::r);
                const __m128i Imag = _mm_set1_epi32(imag.a);
                mint ww = one,xx = one,wx = one;
                for(int jh = 0; jh < u;) {
                    if(jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = v;
                        for(; j0 < je; j0 += 4,j1 += 4,j2 += 4,j3 += 4) {
                            const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
                            const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
                            const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
                            const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
                            const __m128i T0P2 = montgomery_add_128(T0,T2,m2,m0);
                            const __m128i T1P3 = montgomery_add_128(T1,T3,m2,m0);
                            const __m128i T0M2 = montgomery_sub_128(T0,T2,m2,m0);
                            const __m128i T1M3 = montgomery_mul_128(
                                montgomery_sub_128(T1,T3,m2,m0),Imag,r,m1);
                            _mm_storeu_si128((__m128i *)(a + j0),
                                montgomery_add_128(T0P2,T1P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j1),
                                montgomery_sub_128(T0P2,T1P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j2),
                                montgomery_add_128(T0M2,T1M3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j3),
                                montgomery_sub_128(T0M2,T1M3,m2,m0));
                        }
                    }
                    else {
                        ww = xx * xx,wx = ww * xx;
                        const __m128i WW = _mm_set1_epi32(ww.a);
                        const __m128i WX = _mm_set1_epi32(wx.a);
                        const __m128i XX = _mm_set1_epi32(xx.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for(; j0 < je; j0 += 4,j1 += 4,j2 += 4,j3 += 4) {
                            const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
                            const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
                            const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
                            const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
                            const __m128i MT1 = montgomery_mul_128(T1,XX,r,m1);
                            const __m128i MT2 = montgomery_mul_128(T2,WW,r,m1);
                            const __m128i MT3 = montgomery_mul_128(T3,WX,r,m1);
                            const __m128i T0P2 = montgomery_add_128(T0,MT2,m2,m0);
                            const __m128i T1P3 = montgomery_add_128(MT1,MT3,m2,m0);
                            const __m128i T0M2 = montgomery_sub_128(T0,MT2,m2,m0);
                            const __m128i T1M3 = montgomery_mul_128(
                                montgomery_sub_128(MT1,MT3,m2,m0),Imag,r,m1);
                            _mm_storeu_si128((__m128i *)(a + j0),
                                montgomery_add_128(T0P2,T1P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j1),
                                montgomery_sub_128(T0P2,T1P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j2),
                                montgomery_add_128(T0M2,T1M3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j3),
                                montgomery_sub_128(T0M2,T1M3,m2,m0));
                        }
                    }
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            }
            else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m1 = _mm256_set1_epi32(mod);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                const __m256i r = _mm256_set1_epi32(mint::r);
                const __m256i Imag = _mm256_set1_epi32(imag.a);
                mint ww = one,xx = one,wx = one;
                for(int jh = 0; jh < u;) {
                    if(jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = v;
                        for(; j0 < je; j0 += 8,j1 += 8,j2 += 8,j3 += 8) {
                            const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                            const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                            const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
                            const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
                            const __m256i T0P2 = montgomery_add_256(T0,T2,m2,m0);
                            const __m256i T1P3 = montgomery_add_256(T1,T3,m2,m0);
                            const __m256i T0M2 = montgomery_sub_256(T0,T2,m2,m0);
                            const __m256i T1M3 = montgomery_mul_256(
                                montgomery_sub_256(T1,T3,m2,m0),Imag,r,m1);
                            _mm256_storeu_si256((__m256i *)(a + j0),
                                montgomery_add_256(T0P2,T1P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j1),
                                montgomery_sub_256(T0P2,T1P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j2),
                                montgomery_add_256(T0M2,T1M3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j3),
                                montgomery_sub_256(T0M2,T1M3,m2,m0));
                        }
                    }
                    else {
                        ww = xx * xx,wx = ww * xx;
                        const __m256i WW = _mm256_set1_epi32(ww.a);
                        const __m256i WX = _mm256_set1_epi32(wx.a);
                        const __m256i XX = _mm256_set1_epi32(xx.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for(; j0 < je; j0 += 8,j1 += 8,j2 += 8,j3 += 8) {
                            const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                            const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                            const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
                            const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
                            const __m256i MT1 = montgomery_mul_256(T1,XX,r,m1);
                            const __m256i MT2 = montgomery_mul_256(T2,WW,r,m1);
                            const __m256i MT3 = montgomery_mul_256(T3,WX,r,m1);
                            const __m256i T0P2 = montgomery_add_256(T0,MT2,m2,m0);
                            const __m256i T1P3 = montgomery_add_256(MT1,MT3,m2,m0);
                            const __m256i T0M2 = montgomery_sub_256(T0,MT2,m2,m0);
                            const __m256i T1M3 = montgomery_mul_256(
                                montgomery_sub_256(MT1,MT3,m2,m0),Imag,r,m1);
                            _mm256_storeu_si256((__m256i *)(a + j0),
                                montgomery_add_256(T0P2,T1P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j1),
                                montgomery_sub_256(T0P2,T1P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j2),
                                montgomery_add_256(T0M2,T1M3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j3),
                                montgomery_sub_256(T0M2,T1M3,m2,m0));
                        }
                    }
                    xx *= dw[__builtin_ctz((jh += 4))];
                }
            }
            u <<= 2;
            v >>= 2;
        }
    }

    __attribute__((target("avx2"))) void intt(mint *a,int n,
        int normalize = true) {
        int k = n ? __builtin_ctz(n) : 0;
        if(k == 0) return;
        if(k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            if(normalize) {
                a[0] *= mint(2).inverse();
                a[1] *= mint(2).inverse();
            }
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while(u) {
            if(v == 1) {
                mint ww = one,xx = one,yy = one;
                u <<= 2;
                for(int jh = 0; jh < u;) {
                    ww = xx * xx,yy = xx * imag;
                    mint t0 = a[jh + 0],t1 = a[jh + 1];
                    mint t2 = a[jh + 2],t3 = a[jh + 3];
                    mint t0p1 = t0 + t1,t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx,t2m3 = (t2 - t3) * yy;
                    a[jh + 0] = t0p1 + t2p3,a[jh + 2] = (t0p1 - t2p3) * ww;
                    a[jh + 1] = t0m1 + t2m3,a[jh + 3] = (t0m1 - t2m3) * ww;
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            }
            else if(v == 4) {
                const __m128i m0 = _mm_set1_epi32(0);
                const __m128i m1 = _mm_set1_epi32(mod);
                const __m128i m2 = _mm_set1_epi32(mod + mod);
                const __m128i r = _mm_set1_epi32(mint::r);
                const __m128i Imag = _mm_set1_epi32(imag.a);
                mint ww = one,xx = one,yy = one;
                u <<= 2;
                for(int jh = 0; jh < u;) {
                    if(jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = v + v;
                        int j3 = j2 + v;
                        for(; j0 < v; j0 += 4,j1 += 4,j2 += 4,j3 += 4) {
                            const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
                            const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
                            const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
                            const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
                            const __m128i T0P1 = montgomery_add_128(T0,T1,m2,m0);
                            const __m128i T2P3 = montgomery_add_128(T2,T3,m2,m0);
                            const __m128i T0M1 = montgomery_sub_128(T0,T1,m2,m0);
                            const __m128i T2M3 = montgomery_mul_128(
                                montgomery_sub_128(T2,T3,m2,m0),Imag,r,m1);
                            _mm_storeu_si128((__m128i *)(a + j0),
                                montgomery_add_128(T0P1,T2P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j2),
                                montgomery_sub_128(T0P1,T2P3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j1),
                                montgomery_add_128(T0M1,T2M3,m2,m0));
                            _mm_storeu_si128((__m128i *)(a + j3),
                                montgomery_sub_128(T0M1,T2M3,m2,m0));
                        }
                    }
                    else {
                        ww = xx * xx,yy = xx * imag;
                        const __m128i WW = _mm_set1_epi32(ww.a);
                        const __m128i XX = _mm_set1_epi32(xx.a);
                        const __m128i YY = _mm_set1_epi32(yy.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for(; j0 < je; j0 += 4,j1 += 4,j2 += 4,j3 += 4) {
                            const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
                            const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
                            const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
                            const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
                            const __m128i T0P1 = montgomery_add_128(T0,T1,m2,m0);
                            const __m128i T2P3 = montgomery_add_128(T2,T3,m2,m0);
                            const __m128i T0M1 = montgomery_mul_128(
                                montgomery_sub_128(T0,T1,m2,m0),XX,r,m1);
                            __m128i T2M3 = montgomery_mul_128(
                                montgomery_sub_128(T2,T3,m2,m0),YY,r,m1);
                            _mm_storeu_si128((__m128i *)(a + j0),
                                montgomery_add_128(T0P1,T2P3,m2,m0));
                            _mm_storeu_si128(
                                (__m128i *)(a + j2),
                                montgomery_mul_128(montgomery_sub_128(T0P1,T2P3,m2,m0),WW,
                                    r,m1));
                            _mm_storeu_si128((__m128i *)(a + j1),
                                montgomery_add_128(T0M1,T2M3,m2,m0));
                            _mm_storeu_si128(
                                (__m128i *)(a + j3),
                                montgomery_mul_128(montgomery_sub_128(T0M1,T2M3,m2,m0),WW,
                                    r,m1));
                        }
                    }
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            }
            else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m1 = _mm256_set1_epi32(mod);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                const __m256i r = _mm256_set1_epi32(mint::r);
                const __m256i Imag = _mm256_set1_epi32(imag.a);
                mint ww = one,xx = one,yy = one;
                u <<= 2;
                for(int jh = 0; jh < u;) {
                    if(jh == 0) {
                        int j0 = 0;
                        int j1 = v;
                        int j2 = v + v;
                        int j3 = j2 + v;
                        for(; j0 < v; j0 += 8,j1 += 8,j2 += 8,j3 += 8) {
                            const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                            const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                            const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
                            const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
                            const __m256i T0P1 = montgomery_add_256(T0,T1,m2,m0);
                            const __m256i T2P3 = montgomery_add_256(T2,T3,m2,m0);
                            const __m256i T0M1 = montgomery_sub_256(T0,T1,m2,m0);
                            const __m256i T2M3 = montgomery_mul_256(
                                montgomery_sub_256(T2,T3,m2,m0),Imag,r,m1);
                            _mm256_storeu_si256((__m256i *)(a + j0),
                                montgomery_add_256(T0P1,T2P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j2),
                                montgomery_sub_256(T0P1,T2P3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j1),
                                montgomery_add_256(T0M1,T2M3,m2,m0));
                            _mm256_storeu_si256((__m256i *)(a + j3),
                                montgomery_sub_256(T0M1,T2M3,m2,m0));
                        }
                    }
                    else {
                        ww = xx * xx,yy = xx * imag;
                        const __m256i WW = _mm256_set1_epi32(ww.a);
                        const __m256i XX = _mm256_set1_epi32(xx.a);
                        const __m256i YY = _mm256_set1_epi32(yy.a);
                        int j0 = jh * v;
                        int j1 = j0 + v;
                        int j2 = j1 + v;
                        int j3 = j2 + v;
                        int je = j1;
                        for(; j0 < je; j0 += 8,j1 += 8,j2 += 8,j3 += 8) {
                            const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                            const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                            const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
                            const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
                            const __m256i T0P1 = montgomery_add_256(T0,T1,m2,m0);
                            const __m256i T2P3 = montgomery_add_256(T2,T3,m2,m0);
                            const __m256i T0M1 = montgomery_mul_256(
                                montgomery_sub_256(T0,T1,m2,m0),XX,r,m1);
                            const __m256i T2M3 = montgomery_mul_256(
                                montgomery_sub_256(T2,T3,m2,m0),YY,r,m1);
                            _mm256_storeu_si256((__m256i *)(a + j0),
                                montgomery_add_256(T0P1,T2P3,m2,m0));
                            _mm256_storeu_si256(
                                (__m256i *)(a + j2),
                                montgomery_mul_256(montgomery_sub_256(T0P1,T2P3,m2,m0),WW,
                                    r,m1));
                            _mm256_storeu_si256((__m256i *)(a + j1),
                                montgomery_add_256(T0M1,T2M3,m2,m0));
                            _mm256_storeu_si256(
                                (__m256i *)(a + j3),
                                montgomery_mul_256(montgomery_sub_256(T0M1,T2M3,m2,m0),WW,
                                    r,m1));
                        }
                    }
                    xx *= dy[__builtin_ctz(jh += 4)];
                }
            }
            u >>= 4;
            v <<= 2;
        }
        if(k & 1) {
            v = 1 << (k - 1);
            if(v < 8) {
                for(int j = 0; j < v; ++j) {
                    mint ajv = a[j] - a[j + v];
                    a[j] += a[j + v];
                    a[j + v] = ajv;
                }
            }
            else {
                const __m256i m0 = _mm256_set1_epi32(0);
                const __m256i m2 = _mm256_set1_epi32(mod + mod);
                int j0 = 0;
                int j1 = v;
                for(; j0 < v; j0 += 8,j1 += 8) {
                    const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
                    const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
                    __m256i naj = montgomery_add_256(T0,T1,m2,m0);
                    __m256i najv = montgomery_sub_256(T0,T1,m2,m0);
                    _mm256_storeu_si256((__m256i *)(a + j0),naj);
                    _mm256_storeu_si256((__m256i *)(a + j1),najv);
                }
            }
        }
        if(normalize) {
            mint invn = mint(n).inverse();
            for(int i = 0; i < n; i++) a[i] *= invn;
        }
    }

    __attribute__((target("avx2"))) void inplace_multiply(
        int l1,int l2,int zero_padding = true) {
        int l = l1 + l2 - 1;
        int M = 4;
        while(M < l) M <<= 1;
        if(zero_padding) {
            for(int i = l1; i < M; i++) buf1_[i] = 0;
            for(int i = l2; i < M; i++) buf2_[i] = 0;
        }
        const __m256i m0 = _mm256_set1_epi32(0);
        const __m256i m1 = _mm256_set1_epi32(mod);
        const __m256i r = _mm256_set1_epi32(mint::r);
        const __m256i N2 = _mm256_set1_epi32(mint::n2);
        for(int i = 0; i < l1; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i *)(buf1_ + i));
            __m256i b = montgomery_mul_256(a,N2,r,m1);
            _mm256_storeu_si256((__m256i *)(buf1_ + i),b);
        }
        for(int i = 0; i < l2; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i *)(buf2_ + i));
            __m256i b = montgomery_mul_256(a,N2,r,m1);
            _mm256_storeu_si256((__m256i *)(buf2_ + i),b);
        }
        ntt(buf1,M);
        ntt(buf2,M);
        for(int i = 0; i < M; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i *)(buf1_ + i));
            __m256i b = _mm256_loadu_si256((__m256i *)(buf2_ + i));
            __m256i c = montgomery_mul_256(a,b,r,m1);
            _mm256_storeu_si256((__m256i *)(buf1_ + i),c);
        }
        intt(buf1,M,false);
        const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
        for(int i = 0; i < l; i += 8) {
            __m256i a = _mm256_loadu_si256((__m256i *)(buf1_ + i));
            __m256i b = montgomery_mul_256(a,INVM,r,m1);
            __m256i c = my256_mulhi_epu32(my256_mullo_epu32(b,r),m1);
            __m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c,m0),m1);
            __m256i e = _mm256_sub_epi32(d,c);
            _mm256_storeu_si256((__m256i *)(buf1_ + i),e);
        }
    }

    void ntt(vector<mint> &a) {
        int M = (int)a.size();
        for(int i = 0; i < M; i++) buf1[i].a = a[i].a;
        ntt(buf1,M);
        for(int i = 0; i < M; i++) a[i].a = buf1[i].a;
    }

    void intt(vector<mint> &a) {
        int M = (int)a.size();
        for(int i = 0; i < M; i++) buf1[i].a = a[i].a;
        intt(buf1,M,true);
        for(int i = 0; i < M; i++) a[i].a = buf1[i].a;
    }

    vector<mint> multiply(const vector<mint> &a,const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if(min<int>(a.size(),b.size()) <= 40) {
            vector<mint> s(l);
            for(int i = 0; i < (int)a.size(); ++i)
                for(int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
            return s;
        }
        int M = 4;
        while(M < l) M <<= 1;
        for(int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a;
        for(int i = (int)a.size(); i < M; ++i) buf1[i].a = 0;
        for(int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a;
        for(int i = (int)b.size(); i < M; ++i) buf2[i].a = 0;
        ntt(buf1,M);
        ntt(buf2,M);
        for(int i = 0; i < M; ++i)
            buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
        intt(buf1,M,false);
        vector<mint> s(l);
        mint invm = mint(M).inverse();
        for(int i = 0; i < l; ++i) s[i] = buf1[i] * invm;
        return s;
    }

    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        for(int i = 0; i < M; i++) buf1[i].a = a[i].a;
        intt(buf1,M);
        mint r = 1,zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for(int i = 0; i < M; i++) buf1[i] *= r,r *= zeta;
        ntt(buf1,M);
        a.resize(2 * M);
        for(int i = 0; i < M; i++) a[M + i].a = buf1[i].a;
    }
};using namespace std;

template <typename mint>
struct FormalPowerSeries : vector<mint> {
    using vector<mint>::vector;
    using FPS = FormalPowerSeries;

    FPS &operator+=(const FPS &r) {
        if(r.size() > this->size()) this->resize(r.size());
        for(int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
        return *this;
    }

    FPS &operator+=(const mint &r) {
        if(this->empty()) this->resize(1);
        (*this)[0] += r;
        return *this;
    }

    FPS &operator-=(const FPS &r) {
        if(r.size() > this->size()) this->resize(r.size());
        for(int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
        return *this;
    }

    FPS &operator-=(const mint &r) {
        if(this->empty()) this->resize(1);
        (*this)[0] -= r;
        return *this;
    }

    FPS &operator*=(const mint &v) {
        for(int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
        return *this;
    }

    FPS &operator/=(const FPS &r) {
        if(this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }

    FPS &operator%=(const FPS &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }

    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator+(const mint &v) const { return FPS(*this) += v; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator-(const mint &v) const { return FPS(*this) -= v; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator*(const mint &v) const { return FPS(*this) *= v; }
    FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
    FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
    FPS operator-() const {
        FPS ret(this->size());
        for(int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
        return ret;
    }

    void shrink() {
        while(this->size() && this->back() == mint(0)) this->pop_back();
    }

    FPS rev() const {
        FPS ret(*this);
        reverse(begin(ret),end(ret));
        return ret;
    }

    FPS dot(FPS r) const {
        FPS ret(min(this->size(),r.size()));
        for(int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
        return ret;
    }

    FPS pre(int sz) const {
        return FPS(begin(*this),begin(*this) + min((int)this->size(),sz));
    }

    FPS operator>>(int sz) const {
        if((int)this->size() <= sz) return {};
        FPS ret(*this);
        ret.erase(ret.begin(),ret.begin() + sz);
        return ret;
    }

    FPS operator<<(int sz) const {
        FPS ret(*this);
        ret.insert(ret.begin(),sz,mint(0));
        return ret;
    }

    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0,n - 1));
        for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * mint(i);
        return ret;
    }

    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = mint(0);
        for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / mint(i + 1);
        return ret;
    }

    mint eval(mint x) const {
        mint r = 0,w = 1;
        for(auto &v : *this) r += w * v,w *= x;
        return r;
    }

    FPS log(int deg = -1) const {
        assert((*this)[0] == mint(1));
        if(deg == -1) deg = (int)this->size();
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }

    FPS pow(int64_t k,int deg = -1) const {
        const int n = (int)this->size();
        if(deg == -1) deg = n;
        for(int i = 0; i < n; i++) {
            if((*this)[i] != mint(0)) {
                if(i * k > deg) return FPS(deg,mint(0));
                mint rev = mint(1) / (*this)[i];
                FPS ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
                ret = (ret << (i * k)).pre(deg);
                if((int)ret.size() < deg) ret.resize(deg,mint(0));
                return ret;
            }
        }
        return FPS(deg,mint(0));
    }

    static void *ntt_ptr;
    static void set_fft();
    FPS &operator*=(const FPS &r);
    void ntt();
    void intt();
    void ntt_doubling();
    static int ntt_pr();
    FPS inv(int deg = -1) const;
    FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/formal-power-series.md
 */

template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
    if(!ntt_ptr) ntt_ptr = new NTT<mint>;
}

template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint>& r) {
    if(this->empty() || r.empty()) {
        this->clear();
        return *this;
    }
    set_fft();
    auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this,r);
    return *this = FormalPowerSeries<mint>(ret.begin(),ret.end());
}

template <typename mint>
void FormalPowerSeries<mint>::ntt() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::intt() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}

template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}

template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
    set_fft();
    return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
    assert((*this)[0] != mint(0));
    if(deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> res(deg);
    res[0] = {mint(1) / (*this)[0]};
    for(int d = 1; d < deg; d <<= 1) {
        FormalPowerSeries<mint> f(2 * d),g(2 * d);
        for(int j = 0; j < min((int)this->size(),2 * d); j++) f[j] = (*this)[j];
        for(int j = 0; j < d; j++) g[j] = res[j];
        f.ntt();
        g.ntt();
        for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
        f.intt();
        for(int j = 0; j < d; j++) f[j] = 0;
        f.ntt();
        for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
        f.intt();
        for(int j = d; j < min(2 * d,deg); j++) res[j] = -f[j];
    }
    return res.pre(deg);
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
    assert((*this).size() == 0 || (*this)[0] == mint(0));
    if(deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> ret({mint(1)});
    for(int i = 1; i < deg; i <<= 1) {
        ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);
    }
    return ret.pre(deg);
}

using namespace std;

template <typename T>
struct Binomial {
    vector<T> fac_,finv_,inv_;
    Binomial(int MAX): fac_(MAX + 10),finv_(MAX + 10),inv_(MAX + 10) {
        MAX += 9;
        fac_[0] = finv_[0] = inv_[0] = 1;
        for(int i = 1; i <= MAX; i++) fac_[i] = fac_[i - 1] * i;
        finv_[MAX] = fac_[MAX].inverse();
        for(int i = MAX - 1; i > 0; i--) finv_[i] = finv_[i + 1] * (i + 1);
        for(int i = 1; i <= MAX; i++) inv_[i] = finv_[i] * fac_[i - 1];
    }

    inline T fac(int i) const { return fac_[i]; }
    inline T finv(int i) const { return finv_[i]; }
    inline T inv(int i) const { return inv_[i]; }

    T C(int n,int r) const {
        if(n < r || r < 0) return T(0);
        return fac_[n] * finv_[n - r] * finv_[r];
    }

    T C_naive(int n,int r) const {
        if(n < r || r < 0) return T(0);
        T ret = 1;
        for(T i = 1; i <= r; i += T(1)) {
            ret *= n--;
            ret *= i.inverse();
        }
        return ret;
    }

    T P(int n,int r) const {
        if(n < r || r < 0) return T(0);
        return fac_[n] * finv_[n - r];
    }

    T H(int n,int r) const {
        if(n < 0 || r < 0) return (0);
        return r == 0 ? 1 : C(n + r - 1,r);
    }
};

// calculate F(x + a)
template <typename mint>
FormalPowerSeries<mint> TaylorShift(FormalPowerSeries<mint> f,mint a,
    Binomial<mint>& C) {
    using fps = FormalPowerSeries<mint>;
    assert(C.fac_.size() >= f.size() + 1);
    int N = f.size();
    for(int i = 0; i < N; i++) f[i] *= C.fac(i);
    reverse(begin(f),end(f));
    fps g(N,mint(1));
    for(int i = 1; i < N; i++) g[i] = g[i - 1] * a * C.inv(i);
    f = (f * g).pre(N);
    reverse(begin(f),end(f));
    for(int i = 0; i < N; i++) f[i] *= C.finv(i);
    return f;
}

/**
 * @brief 平行移動
 * @docs docs/fps-taylor-shift.md
 */

using namespace std;

namespace fastio {
    static constexpr int SZ = 1 << 17;
    char ibuf[SZ],obuf[SZ];
    int pil = 0,pir = 0,por = 0;

    struct Pre {
        char num[40000];
        constexpr Pre(): num() {
            for(int i = 0; i < 10000; i++) {
                int n = i;
                for(int j = 3; j >= 0; j--) {
                    num[i * 4 + j] = n % 10 + '0';
                    n /= 10;
                }
            }
        }
    } constexpr pre;

    inline void load() {
        memcpy(ibuf,ibuf + pil,pir - pil);
        pir = pir - pil + fread(ibuf + pir - pil,1,SZ - pir + pil,stdin);
        pil = 0;
    }
    inline void flush() {
        fwrite(obuf,1,por,stdout);
        por = 0;
    }

    inline void rd(char& c) { c = ibuf[pil++]; }
    template <typename T>
    inline void rd(T& x) {
        if(pil + 32 > pir) load();
        char c;
        do
            c = ibuf[pil++];
        while(c < '-');
        bool minus = 0;
        if(c == '-') {
            minus = 1;
            c = ibuf[pil++];
        }
        x = 0;
        while(c >= '0') {
            x = x * 10 + (c & 15);
            c = ibuf[pil++];
        }
        if(minus) x = -x;
    }

    inline void wt(char c) { obuf[por++] = c; }
    template <typename T>
    inline void wt(T x) {
        if(por > SZ - 32) flush();
        if(!x) {
            obuf[por++] = '0';
            return;
        }
        if(x < 0) {
            obuf[por++] = '-';
            x = -x;
        }
        int i = 12;
        char buf[16];
        while(x >= 10000) {
            memcpy(buf + i,pre.num + (x % 10000) * 4,4);
            x /= 10000;
            i -= 4;
        }
        int d = x < 100 ? (x < 10 ? 1 : 2) : (x < 1000 ? 3 : 4);
        memcpy(obuf + por,pre.num + x * 4 + 4 - d,d);
        por += d;
        memcpy(obuf + por,buf + i + 4,12 - i);
        por += 12 - i;
    }

    struct Dummy {
        Dummy() { atexit(flush); }
    } dummy;

}  // namespace fastio
using fastio::rd;
using fastio::wt;
using namespace std;

template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static constexpr u32 get_r() {
        u32 ret = mod;
        for(i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(r * mod == 1,"invalid, r * mod != 1");
    static_assert(mod < (1 << 30),"invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1,"invalid, mod % 2 == 0");

    u32 a;

    constexpr LazyMontgomeryModInt(): a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
        : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }

    constexpr mint &operator+=(const mint &b) {
        if(i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator-=(const mint &b) {
        if(i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }

    constexpr mint pow(u64 n) const {
        mint ret(1),mul(*this);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    constexpr mint inverse() const { return pow(mod - 2); }

    friend ostream &operator<<(ostream &os,const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is,mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }

    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static constexpr u32 get_mod() { return mod; }
};


template <typename mint>
FormalPowerSeries<mint> Stirling1st(int N,Binomial<mint> &C) {
    using fps = FormalPowerSeries<mint>;
    if(N <= 0) return fps{1};
    int lg = 31 - __builtin_clz(N);
    fps f = {0, 1};
    for(int i = lg - 1; i >= 0; i--) {
        int n = N >> i;
        f *= TaylorShift(f,mint(n >> 1),C);
        if(n & 1) f = (f << 1) + f * (n - 1);
    }
    return f;
}

template <typename mint>
FormalPowerSeries<mint> Stirling2nd(int N,Binomial<mint> &C) {
    using fps = FormalPowerSeries<mint>;
    fps f(N + 1),g(N + 1);
    for(int i = 0; i <= N; i++) {
        f[i] = mint(i).pow(N) * C.finv(i);
        g[i] = (i & 1) ? -C.finv(i) : C.finv(i);
    }
    return (f * g).pre(N + 1);
}

template <typename mint>
FormalPowerSeries<mint> BernoulliEGF(int N,Binomial<mint> &C) {
    using fps = FormalPowerSeries<mint>;
    fps f(N + 1);
    for(int i = 0; i <= N; i++) f[i] = C.finv(i + 1);
    return f.inv(N + 1);
}

template <typename mint>
FormalPowerSeries<mint> SamplePointShift(FormalPowerSeries<mint>& y,mint t,
    int m = -1) {
    if(m == -1) m = y.size();
    long long T = t.get();
    int k = (int)y.size() - 1;
    T %= mint::get_mod();
    if(T <= k) {
        FormalPowerSeries<mint> ret(m);
        int ptr = 0;
        for(int64_t i = T; i <= k and ptr < m; i++) {
            ret[ptr++] = y[i];
        }
        if(k + 1 < T + m) {
            auto suf = SamplePointShift<mint>(y,k + 1,m - ptr);
            for(int i = k + 1; i < T + m; i++) {
                ret[ptr++] = suf[i - (k + 1)];
            }
        }
        return ret;
    }
    if(T + m > mint::get_mod()) {
        auto pref = SamplePointShift<mint>(y,T,mint::get_mod() - T);
        auto suf = SamplePointShift<mint>(y,0,m - pref.size());
        copy(begin(suf),end(suf),back_inserter(pref));
        return pref;
    }

    FormalPowerSeries<mint> finv(k + 1,1),d(k + 1);
    for(int i = 2; i <= k; i++) finv[k] *= i;
    finv[k] = mint(1) / finv[k];
    for(int i = k; i >= 1; i--) finv[i - 1] = finv[i] * i;
    for(int i = 0; i <= k; i++) {
        d[i] = finv[i] * finv[k - i] * y[i];
        if((k - i) & 1) d[i] = -d[i];
    }

    FormalPowerSeries<mint> h(m + k);
    for(int i = 0; i < m + k; i++) {
        h[i] = mint(1) / (T - k + i);
    }

    auto dh = d * h;

    FormalPowerSeries<mint> ret(m);
    mint cur = T;
    for(int i = 1; i <= k; i++) cur *= T - i;
    for(int i = 0; i < m; i++) {
        ret[i] = cur * dh[k + i];
        cur *= T + i + 1;
        cur *= h[i];
    }
    return ret;
}


ll modinv(ll A,ll M){
    //A*r+B*n=gcd(A,B)
    A %= M;
    if(A == 0 || __gcd(A,M) != 1){
        //cout << "Error modinv(" << A << "," << M << ")" << endl;
        return -1;
    }
    ll B = M,U = 1,V = 0;
    while(B){
        ll T = A / B;
        A -= T * B;
        swap(A,B);
        U -= T * V;
        swap(U,V);
    }
    U %= M;
    if(U < 0) U += M;
    return U;
}

template <typename mint>
mint factorial(int n) {
    if(n <= 1) return 1;
    using fps = FormalPowerSeries<mint>;
    long long v = 1;
    while(v * v < n) v *= 2;
    mint iv = mint(v).inverse();
    fps G{1, v + 1};
    for(long long d = 1; d != v; d <<= 1) {
        fps G1 = SamplePointShift(G,mint(d) * iv);
        fps G2 = SamplePointShift(G,mint(d * v + v) * iv);
        fps G3 = SamplePointShift(G,mint(d * v + d + v) * iv);
        for(int i = 0; i <= d; i++) G[i] *= G1[i],G2[i] *= G3[i];
        copy(begin(G2),end(G2) - 1,back_inserter(G));
    }
    mint res = 1;
    long long i = 0;
    while(i + v <= n) res *= G[i / v],i += v;
    while(i < n) res *= ++i;
    return res;
}

int main(){
    constexpr int MOD9 = 998244353;
    using mint = LazyMontgomeryModInt<MOD9>;
    Binomial<mint> C(1530000);

    auto seq = BernoulliEGF(1000010,C);
    vector<ll> B(1000010);
    for(int i = 0; i < 1000010; i++) {
        B[i] = ((seq[i] * C.fac(i)).get());
    }
    wt('\n');
    ll N,M;
    ll n,k;
    cin >> N >> M;
    n = N;
    k = M;
    N -= 1;
    /*for(ll i = 0;i <= N;i++){
        for(ll j = 0;j <= K;j++){
            ll x = 0;
            for(ll p = 1;p < i;p++){
                x += modpow(p,j,MOD) * (i - p);
            }
            cout << x << " ";
        }
        cout << endl;
    }*/
    COMinit(5000000);
    ll a1 = 0;
    vector<ll> modp(M + 200,1);
    for(ll i = 1;i <= M + 100;i++) modp[i] = (modp[i - 1] * (N + 1 % MOD9)) % MOD9;
    for(ll i = 0;i <= M;i++){
        ll x = COM(M + 1,i) * B[i] % MOD9;
        x *= modp[M + 1 - i];
        x %= MOD9;
        a1 += x;
        a1 %= MOD9;
        if(a1 < 0) a1 += MOD9;
    }
    a1 *= N + 1;
    a1 %= MOD9;
    a1 *= modinv(M + 1,MOD9);
    a1 %= MOD9;
    ll a2 = 0;
    for(ll i = 0;i <= M + 1;i++){
        ll x = COM(M + 2,i) * B[i] % MOD9;
        x *= modp[M + 2 - i];
        x %= MOD9;
        a2 += x;
        a2 %= MOD9;
        if(a2 < 0) a2 += MOD9;
    }
    a2 *= modinv(M + 2,MOD9);
    a2 %= MOD9;
    if(a2 < 0) a2 += MOD9;

    ll ans = a1 - a2;
    ans %= MOD9;
    if(ans < 0) ans += MOD9;
    //cerr << ans << endl;


    
    ans *= factorial<mint>(n - 1).get();

    //for(ll i = 1;i <= n - 1;i++) ans = (ans * i) % MOD;
    ans *= 2;
    ans %= MOD;
    if(ans < 0) ans += MOD;
    cout << ans << endl;
}