#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;

void solve();
int main() { solve(); }

#pragma endregion
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; }
};
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) {
    if (a.size() == 0 && b.size() == 0) return vector<mint>{};
    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 mint = LazyMontgomeryModInt<998244353>;

NTT<mint> ntt;

void fft(V<V<mint>> &a) {
  int N = sz(a);
  int M = sz(a[0]);
  rep(i, N) ntt.ntt(a[i]);
  V<mint> b(N);
  rep(j, M) {
    rep(i, N) b[i] = a[i][j];
    ntt.ntt(b);
    rep(i, N) a[i][j] = b[i];
  }
}

void ifft(V<V<mint>> &a) {
  int N = sz(a);
  int M = sz(a[0]);
  V<mint> b(N);
  rep(j, M) {
    rep(i, N) b[i] = a[i][j];
    ntt.intt(b);
    rep(i, N) a[i][j] = b[i];
  }
  rep(i, N) ntt.intt(a[i]);
}

void solve() {
  inl(x, y, t, a, b, c, d);
  int N = 1 << x;
  int M = 1 << y;

  V<V<mint>> A(N * 2, V<mint>(M * 2, 0));
  A[0][0] = A[1][0] = A[0][1] = A[2 * N - 1][0] = A[0][2 * M - 1] = 1;
  V<V<mint>> B(N * 2, V<mint>(M * 2, 0));
  B[a][b] = 1;
  trc(A);
  fft(A);
  trc(A);
  trc(B);
  fft(B);
  trc(B);
  trc(t);
  each(v, A) each(w, v) w = w.pow(t);
  rep(i, 2 * N) rep(j, 2 * M) A[i][j] *= B[i][j];
  trc(A);
  ifft(A);
  trc(A);
  trc(A[c][d]);
  trc(A[2 * N - c][d]);
  trc(A[c][2 * M - d]);
  trc(A[2 * N - c][2 * M - d]);
  out(A[c][d] - A[2 * N - c][d] - A[c][2 * M - d] + A[2 * N - c][2 * M - d]);
}