#include <bits/stdc++.h>  // clang-format off
#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 ini(...) int __VA_ARGS__; in(__VA_ARGS__)
#define inl(...) long long __VA_ARGS__; in(__VA_ARGS__)
#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)

#ifdef ONLINE_JUDGE
  #define rep(i,N) for(int i = 0; i < (int)(N); i++)
  #define repr(i,N) for(int i = (int)(N) - 1; i >= 0; i--)
  #define rep1(i,N) for(int i = 1; i <= (int)(N) ; i++)
  #define repr1(i,N) for(int i = (N) ; (int)(i) > 0 ; i--)
#else
  #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--)
#endif

using namespace std; void solve();
using ll = long long; template<class T = ll> using V = vector<T>;
using vi = V<int>; using vl = V<>; using vvi = V< V<int> >;
constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1;

#ifdef NyaanDebug
  #include "NyaanDebug.h"
  #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 << "name : " << #v << "\n"; int cnt = 0; each(x , v){cerr << (cnt++) << " : "; trc(x); } } while(0)
#else
  #define trc(...)
  #define trca(...)
  #define trcc(...)
  int main(){solve();}
#endif

#define inc(...) char __VA_ARGS__; in(__VA_ARGS__)
#define in2(s,t)     rep(i,sz(s)){in(s[i] , t[i]);}
#define in3(s,t,u)   rep(i,sz(s)){in(s[i] , t[i] , u[i]);}
#define in4(s,t,u,v) rep(i,sz(s)){in(s[i] , t[i] , u[i] , v[i]);}
using vd = V<double>; using vs = V<string>; using vvl = V< V<> >;
template<typename T,typename U>ll ceil(T a,U b){return (a + b - 1) / b;}

using P = pair<int,int>; using vp = V<P>;
constexpr int MOD = /**/ 1000000007; //*/ 998244353;
// clang-format on
/////////////////////////

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< MOD >;
using mint = modint;

namespace FastFourierTransform {
  using real = double;

  struct C {
    real x, y;

    C() : x(0), y(0) {}

    C(real x, real y) : x(x), y(y) {}

    inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

    inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

    inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

    inline C conj() const { return C(x, -y); }
  };

  const real PI = acosl(-1);
  int base = 1;
  vector< C > rts = { {0, 0},
                     {1, 0} };
  vector< int > rev = {0, 1};


  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while(base < nbase) {
      real angle = PI * 2.0 / (1 << (base + 1));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        real angle_i = angle * (2 * i + 1 - (1 << base));
        rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
      }
      ++base;
    }
  }

  void fft(vector< C > &a, int n) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          C z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }

  vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
    int need = (int) a.size() + (int) b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < sz; i++) {
      int x = (i < (int) a.size() ? a[i] : 0);
      int y = (i < (int) b.size() ? b[i] : 0);
      fa[i] = C(x, y);
    }
    fft(fa, sz);
    C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
      fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
      fa[i] = z;
    }
    for(int i = 0; i < (sz >> 1); i++) {
      C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
      C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
      fa[i] = A0 + A1 * s;
    }
    fft(fa, sz >> 1);
    vector< int64_t > ret(need);
    for(int i = 0; i < need; i++) {
      ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
    }
    return ret;
  }
};

template< typename T >
struct ArbitraryModConvolution {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolution() = default;

  vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
    if(need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    vector< C > fa(sz);
    for(int i = 0; i < (int)a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
    }
    fft(fa, sz);
    vector< C > fb(sz);
    if(a == b) {
      fb = fa;
    } else {
      for(int i = 0; i < (int)b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for(int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if(i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    vector< T > ret(need);
    for(int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
  }
};

template< int mod >
struct NumberTheoreticTransform {

  int base, max_base, root;
  vector< int > rev, rts;

  NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while(tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;
    assert(mod_pow(root, mod - 1) == 1);
    root = mod_pow(root, (mod - 1) >> max_base);
  }

  inline int mod_pow(int x, int n) {
    int ret = 1;
    while(n > 0) {
      if(n & 1) ret = mul(ret, x);
      x = mul(x, x);
      n >>= 1;
    }
    return ret;
  }

  inline int inverse(int x) {
    return mod_pow(x, mod - 2);
  }

  inline unsigned add(unsigned x, unsigned y) {
    x += y;
    if(x >= mod) x -= mod;
    return x;
  }

  inline unsigned mul(unsigned a, unsigned b) {
    return 1ull * a * b % (unsigned long long) mod;
  }

  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while(base < nbase) {
      int z = mod_pow(root, 1 << (max_base - 1 - base));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = mul(rts[i], z);
      }
      ++base;
    }
  }


  void ntt(vector< int > &a) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          int z = mul(a[i + j + k], rts[j + k]);
          a[i + j + k] = add(a[i + j], mod - z);
          a[i + j] = add(a[i + j], z);
        }
      }
    }
  }


  vector< int > multiply(vector< int > a, vector< int > b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    int inv_sz = inverse(sz);
    for(int i = 0; i < sz; i++) {
      a[i] = mul(a[i], mul(b[i], inv_sz));
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }

  vector<modint> multiply_for_fps(const vector<modint> &a,const vector<modint> &b){
    vector<int> A(a.size()) , B(b.size());
    for(int i = 0;i < (int)a.size(); i++) A[i] = a[i].x;
    for(int i = 0;i < (int)b.size(); i++) B[i] = b[i].x;
    auto C = multiply( A , B );
    vector<modint> ret(C.size());
    for(int i = 0; i < (int)C.size() ;i++) ret[i].x = C[i];
    return ret;
  }
};


template< typename T >
struct FormalPowerSeries : vector< T > {
  using vector< T >::vector;
  using P = FormalPowerSeries;

  using MULT = function< P(P, P) >;

  static MULT &get_mult() {
    static MULT mult = nullptr;
    return mult;
  }

  static void set_fft(MULT f) {
    get_mult() = f;
  }

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

  P operator+(const P &r) const { return P(*this) += r; }

  P operator+(const T &v) const { return P(*this) += v; }

  P operator-(const P &r) const { return P(*this) -= r; }

  P operator-(const T &v) const { return P(*this) -= v; }

  P operator*(const P &r) const { return P(*this) *= r; }

  P operator*(const T &v) const { return P(*this) *= v; }

  P operator/(const P &r) const { return P(*this) /= r; }

  P operator%(const P &r) const { return P(*this) %= r; }

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

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

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

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

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

  P &operator*=(const P &r) {
    if(this->empty() || r.empty()) {
      this->clear();
      return *this;
    }
    assert(get_mult() != nullptr);
    return *this = get_mult()(*this, r);
  }

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

  P operator-() const {
    P ret(this->size());
    for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
    return ret;
  }

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

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

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

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

  P rev(int deg = -1) const {
    P ret(*this);
    if(deg != -1) ret.resize(deg, T(0));
    reverse(begin(ret), end(ret));
    return ret;
  }

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

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

  // F(0) must not be 0
  P inv(int deg = -1) const {
    assert(((*this)[0]) != T(0));
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    P ret({T(1) / (*this)[0]});
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
    }
    return ret.pre(deg);
  }

  // F(0) must be 1
  P log(int deg = -1) const {
    assert((*this)[0] == 1);
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  P sqrt(int deg = -1) const {
    const int n = (int) this->size();
    if(deg == -1) deg = n;

    if((*this)[0] == T(0)) {
      for(int i = 1; i < n; i++) {
        if((*this)[i] != T(0)) {
          if(i & 1) return {};
          if(deg - i / 2 <= 0) break;
          auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2);
          if(ret.size() < deg) ret.resize(deg, T(0));
          return ret;
        }
      }
      return P(deg, 0);
    }

    P ret({T(1)});
    T inv2 = T(1) / T(2);
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
    }
    return ret.pre(deg);
  }

  // F(0) must be 0
  P exp(int deg = -1) const {
    assert((*this)[0] == T(0));
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    P ret({T(1)});
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
    }
    return ret.pre(deg);
  }

  P pow(int64_t k, int deg = -1) const {
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    for(int i = 0; i < n; i++) {
      if((*this)[i] != T(0)) {
        T rev = T(1) / (*this)[i];
        P C(*this * rev);
        P D(n - i);
        for(int j = i; j < n; j++) D[j - i] = C[j];
        D = (D.log() * k).exp() * (*this)[i].pow(k);
        P E(deg);
        if(i * k > deg) return E;
        auto S = i * k;
        for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];
        return E;
      }
    }
    return *this;
  }

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

using FPS = FormalPowerSeries< modint >;

// fにa * x^n + bを掛ける
void mul_simple(FPS &f,modint a ,int n, modint b){
  for(int i = (int)f.size() - 1 ; i >= 0 ; i--){
    f[i] *= b;
    if(i >= n) f[i] += f[i - n] * a; 
  }
}

// fからa * x^n + bを割る
void div_simple(FPS &f,modint a,int n,modint b){
  for(int i = 0 ; i < (int)f.size() ; i++){
    f[i] /= b;
    if(i + n < (int)f.size() ) f[n + i] -= f[i] * a; 
  }
}

// f / gをdeg(f)次まで求める
FPS div_(FPS &f , FPS g){
  int n = f.size();
  return (f * g.inv(n)).pre(n);
}


// solve関数内で
//
// FPS::set_fft(mul);
//
// とすること。

/**
NumberTheoreticTransform<MOD> ntt;
auto mul = [&](const FPS::P &a, const FPS::P &b) {
  auto ret =ntt.multiply_for_fps(a , b);
  return FPS::P(ret.begin(), ret.end());
};
/*///
ArbitraryModConvolution< modint > fft;
auto mul = [&](const FPS::P &a, const FPS::P &b) {
  auto ret = fft.multiply(a, b);
  return FPS::P(ret.begin(), ret.end());
};
//*/

// 下記のリンクを実装(kitamasa法のモンゴメリ乗算を使わない版)
// http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
// k項間漸化式のa_Nを求める O(k log k log N)
// N ... 求めたい項　(0-indexed)
// Q ... 漸化式 (1 - \sum_i c_i x^i)の形
// a ... 初期解 (a_0 , a_1 , ... , a_k-1)
// x^N を fでわった剰余を求め、aと内積を取る
modint kitamasa(ll N, FPS &Q, FPS &a){
  int k = Q.size() - 1;
  assert( (int)a.size() == k );
  FPS P = a * Q; P.resize(k);
  while(N){
    auto Q2 = Q;
    for(int i = 1; i < (int)Q2.size(); i += 2) Q2[i].x = MOD - Q2[i].x;
    auto S = P * Q2;
    auto T = Q * Q2;
    if(N & 1){
      for(int i = 1 ; i < (int)S.size() ; i += 2) P[i>>1].x = S[i].x;
      for(int i = 0 ; i < (int)T.size() ; i += 2) Q[i>>1].x = T[i].x;
    }
    else{
      for(int i = 0 ; i < (int)S.size() ; i += 2) P[i>>1].x = S[i].x;
      for(int i = 0 ; i < (int)T.size() ; i += 2) Q[i>>1].x = T[i].x;
    }
    N >>= 1;
  }
  return P[0];
}

mint dp[444][444];

namespace fast {
  // XXX fast I/O by rsk0315
  static size_t constexpr buf_size = 1 << 17;
  static size_t constexpr margin = 1;
  static char inbuf[buf_size + margin] = {};
  static char outbuf[buf_size + margin] = {};
  static __attribute__((aligned(8))) char minibuf[32];
  static size_t constexpr int_digits = 20;  // 18446744073709551615
  static uintmax_t constexpr digit_mask = 0x3030303030303030;
  static uintmax_t constexpr first_mask = 0x00FF00FF00FF00FF;
  static uintmax_t constexpr second_mask = 0x0000FFFF0000FFFF;
  static uintmax_t constexpr third_mask = 0x00000000FFFFFFFF;
  static uintmax_t constexpr tenpow[] = {
    1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000
  };
  template <typename Tp>
  using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;

  class scanner {
    char* pos = inbuf;
    char* endpos = inbuf + buf_size;

    void M_read_from_stdin() {
      endpos = inbuf + fread(pos, 1, buf_size, stdin);
    }
    void M_reread_from_stdin() {
      ptrdiff_t len = endpos - pos;
      if (!(inbuf + len <= pos)) return;
      memcpy(inbuf, pos, len);
      char* tmp = inbuf + len;
      endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
      *endpos = 0;
      pos = inbuf;
    }

  public:
    scanner() { M_read_from_stdin(); }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void scan_parallel(Integral& x) {
      // See https://qiita.com/rsk0315_h4x/items/17a9cb12e0de5fd918f4
      if (__builtin_expect(endpos <= pos + int_digits, 0))
        M_reread_from_stdin();
      bool ends = false;
      typename std::make_unsigned<Integral>::type y = 0;
      bool neg = false;
      if (std::is_signed<Integral>::value && *pos == '-') {
        neg = true;
        ++pos;
      }
      do {
        memcpy(minibuf, pos, 8);
        long c = *(long*)minibuf;
        long d = (c & digit_mask) ^ digit_mask;
        int skip = 8;
        int shift = 8;
        if (d) {
          int ctz = __builtin_ctzl(d);
          if (ctz == 4) break;
          c &= (1L << (ctz-5)) - 1;
          int discarded = (68-ctz) / 8;
          shift -= discarded;
          c <<= discarded * 8;
          skip -= discarded;
          ends = true;
        }
        c |= digit_mask;
        c ^= digit_mask;
        c = ((c >> 8) + c*10) & first_mask;
        c = ((c >> 16) + c*100) & second_mask;
        c = ((c >> 32) + c*10000) & third_mask;
        y = y*tenpow[shift] + c;
        pos += skip;
      } while (!ends);
      x = (neg? -y: y);
      ++pos;
    }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void scan_serial(Integral& x) {
      if (__builtin_expect(endpos <= pos + int_digits, 0))
        M_reread_from_stdin();
      bool neg = false;
      if (std::is_signed<Integral>::value && *pos == '-') {
        neg = true;
        ++pos;
      }
      typename std::make_unsigned<Integral>::type y = *pos-'0';
      while (*++pos >= '0') y = (y << 1) + (y << 3) + *pos-'0';
      x = (neg? -y: y);
      ++pos;
    }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    // Use scan_parallel(x) only when x may be too large (about 10^12).
    // Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
    void scan(Integral& x) { scan_serial(x); }

    void scan_serial(std::string& s) {
      // until first whitespace
      s = "";
      do {
        char* startpos = pos;
        while (*pos > ' ') ++pos;
        s += std::string(startpos, pos);
        if (*pos != 0) {
          ++pos;  // skip the space
          break;
        }
        M_reread_from_stdin();
      } while (true);
    }

    void scan(std::string& s) { scan_serial(s); }

    void scan(char& c) {
      if (__builtin_expect(endpos <= pos + 2, 0))
        M_reread_from_stdin();
      c = *pos++;
      ++pos;
    }
  };

  class printer {
    char* pos = outbuf;

    void M_flush_stdout() {
      fwrite(outbuf, 1, pos-outbuf, stdout);
      pos = outbuf;
    }

  public:
    printer() = default;
    ~printer() { M_flush_stdout(); }

    void print(char c) {
      if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
      *pos++ = c;
    }

    template <size_t N>
    void print(char const(&s)[N]) {
      if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
      memcpy(pos, s, N-1);
      pos += N-1;
    }

    void print(char const* s) {
      while (*s != 0) {
        *pos++ = *s++;
        if (pos == outbuf + buf_size) M_flush_stdout();
      }
    }

    template <typename Integral,
              typename enable_if_integral<Integral>::type* = nullptr>
    void print(Integral x) {
      if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
        M_flush_stdout();
      if (x == 0) {
        *pos++ = '0';
        return;
      }
      if (x < 0) {
        *pos++ = '-';
        if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
          switch (sizeof x) {
          case 2: print("32768"); return;
          case 4: print("2147483648"); return;
          case 8: print("9223372036854775808"); return;
          }
        }
        x = -x;
      }
      char* mp = minibuf + sizeof minibuf;
      *--mp = x % 10 + '0';
      size_t len = 1;
      typename std::make_unsigned<Integral>::type y = x / 10;
      while (y > 0) {
        *--mp = y % 10 + '0';
        y /= 10;
        ++len;
      }
      memcpy(pos, mp, len);
      pos += len;
    }

    template <typename Tp>
    void println(Tp const& x) { print(x), print('\n'); }
  };
} // fast::

fast::scanner in;
fast::printer out;


void solve(){
  int N , C;
  in.scan(N);
  in.scan(C);
  
  vi A(N) , B(N);
  rep(i,N) in.scan(A[i]);
  rep(i,N) in.scan(B[i]);
  FPS::set_fft(mul);

  mint beki[444][444];

  rep(i , 401) rep(j , 401){
    if(j) beki[i][j] = beki[i][j - 1] * i;
    else beki[i][j] = 1;
  }
  rep1(i , 400) rep(j , 401){
    beki[i][j] += beki[i - 1][j];
  }

  FPS f{1};

  rep(i , N){
    FPS g(C + 1);
    
    rep(j , C + 1){
      trc( i , j ,A[i] , B[i] , beki[B[i]][j] , beki[A[i] - 1][j]);
      g[j] = beki[B[i]][j] - beki[A[i] - 1][j];
    }
    //trc(g);
    f *= g;
    //trc(f);
    f.resize(C + 1);
  }

  out.println(f[C].x);



  
}

Measured memory_bytes: 1920