#include <bits/stdc++.h>
constexpr int P = 998244353;
using i64 = long long;
int norm(int x) {
  if (x < 0) {
    x += P;
  }
  if (x >= P) {
    x -= P;
  }
  return x;
}
template <class T>
T power(T a, int b) {
  T res = 1;
  for (; b; b /= 2, a *= a) {
    if (b % 2) {
      res *= a;
    }
  }
  return res;
}
struct Z {
  int x;
  Z(int x = 0) : x(norm(x)) {}
  int val() const { return x; }
  Z operator-() const { return Z(norm(P - x)); }
  Z inv() const {
    assert(x != 0);
    return power(*this, P - 2);
  }
  Z &operator*=(const Z &rhs) {
    x = i64(x) * rhs.x % P;
    return *this;
  }
  Z &operator+=(const Z &rhs) {
    x = norm(x + rhs.x);
    return *this;
  }
  Z &operator-=(const Z &rhs) {
    x = norm(x - rhs.x);
    return *this;
  }
  Z &operator/=(const Z &rhs) { return *this *= rhs.inv(); }
  friend Z operator*(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res *= rhs;
    return res;
  }
  friend Z operator+(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res += rhs;
    return res;
  }
  friend Z operator-(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res -= rhs;
    return res;
  }
  friend Z operator/(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res /= rhs;
    return res;
  }
};
std::vector<int> rev;
std::vector<Z> roots{0, 1};
void dft(std::vector<Z> &a) {
  int n = a.size();
  if (int(rev.size()) != n) {
    int k = __builtin_ctz(n) - 1;
    rev.resize(n);
    for (int i = 0; i < n; i++) {
      rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
    }
  }
  for (int i = 0; i < n; i++) {
    if (rev[i] < i) {
      std::swap(a[i], a[rev[i]]);
    }
  }
  if (int(roots.size()) < n) {
    int k = __builtin_ctz(roots.size());
    roots.resize(n);
    while ((1 << k) < n) {
      Z e = power(Z(3), (P - 1) >> (k + 1));
      for (int i = 1 << (k - 1); i < (1 << k); i++) {
        roots[2 * i] = roots[i];
        roots[2 * i + 1] = roots[i] * e;
      }
      k++;
    }
  }
  for (int k = 1; k < n; k *= 2) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        Z u = a[i + j];
        Z v = a[i + j + k] * roots[k + j];
        a[i + j] = u + v;
        a[i + j + k] = u - v;
      }
    }
  }
}
void idft(std::vector<Z> &a) {
  int n = a.size();
  std::reverse(a.begin() + 1, a.end());
  dft(a);
  Z inv = Z(n).inv();
  for (int i = 0; i < n; i++) {
    a[i] *= inv;
  }
}
struct Poly {
  std::vector<Z> a;
  Poly() {}
  Poly(const std::vector<Z> &a) : a(a) {}
  int size() const { return a.size(); }
  void resize(int n) { a.resize(n); }
  Z operator[](int idx) const {
    if (idx < 0 || idx >= size()) {
      return 0;
    }
    return a[idx];
  }
  Z &operator[](int idx) { return a[idx]; }
  Poly mulxk(int k) const {
    auto b = a;
    b.insert(b.begin(), k, 0);
    return Poly(b);
  }
  Poly modxk(int k) const {
    k = std::min(k, size());
    return Poly(std::vector<Z>(a.begin(), a.begin() + k));
  }
  Poly divxk(int k) const {
    if (size() <= k) {
      return Poly();
    }
    return Poly(std::vector<Z>(a.begin() + k, a.end()));
  }
  friend Poly operator+(const Poly &a, const Poly &b) {
    std::vector<Z> res(std::max(a.size(), b.size()));
    for (int i = 0; i < int(res.size()); i++) {
      res[i] = a[i] + b[i];
    }
    return Poly(res);
  }
  friend Poly operator-(const Poly &a, const Poly &b) {
    std::vector<Z> res(std::max(a.size(), b.size()));
    for (int i = 0; i < int(res.size()); i++) {
      res[i] = a[i] - b[i];
    }
    return Poly(res);
  }
  friend Poly operator*(Poly a, Poly b) {
    if (a.size() == 0 || b.size() == 0) {
      return Poly();
    }
    int sz = 1, tot = a.size() + b.size() - 1;
    while (sz < tot) sz *= 2;
    a.a.resize(sz);
    b.a.resize(sz);
    dft(a.a);
    dft(b.a);
    for (int i = 0; i < sz; ++i) {
      a.a[i] = a[i] * b[i];
    }
    idft(a.a);
    a.resize(tot);
    return a;
  }
  friend Poly operator*(Z a, Poly b) {
    for (int i = 0; i < int(b.size()); i++) {
      b[i] *= a;
    }
    return b;
  }
  friend Poly operator*(Poly a, Z b) {
    for (int i = 0; i < int(a.size()); i++) {
      a[i] *= b;
    }
    return a;
  }
  Poly &operator+=(Poly b) { return (*this) = (*this) + b; }
  Poly &operator-=(Poly b) { return (*this) = (*this) - b; }
  Poly &operator*=(Poly b) { return (*this) = (*this) * b; }
  Poly deriv() const {
    if (a.empty()) {
      return Poly();
    }
    std::vector<Z> res(size() - 1);
    for (int i = 0; i < size() - 1; ++i) {
      res[i] = (i + 1) * a[i + 1];
    }
    return Poly(res);
  }
  Poly integr() const {
    std::vector<Z> res(size() + 1);
    for (int i = 0; i < size(); ++i) {
      res[i + 1] = a[i] / (i + 1);
    }
    return Poly(res);
  }
  Poly inv(int m) const {
    Poly x({a[0].inv()});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x * (Poly({2}) - modxk(k) * x)).modxk(k);
    }
    return x.modxk(m);
  }
  Poly log(int m) const { return (deriv() * inv(m)).integr().modxk(m); }
  Poly exp(int m) const {
    Poly x({1});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x * (Poly({1}) - x.log(k) + modxk(k))).modxk(k);
    }
    return x.modxk(m);
  }
  Poly sqrt(int m) const {
    Poly x({1});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
    }
    return x.modxk(m);
  }
  Poly mulT(Poly b) const {
    if (b.size() == 0) {
      return Poly();
    }
    int n = b.size();
    std::reverse(b.a.begin(), b.a.end());
    return ((*this) * b).divxk(n - 1);
  }
  std::vector<Z> eval(std::vector<Z> x) const {
    if (size() == 0) {
      return std::vector<Z>(x.size(), 0);
    }
    const int n = std::max(int(x.size()), size());
    std::vector<Poly> q(4 * n);
    std::vector<Z> ans(x.size());
    x.resize(n);
    std::function<void(int, int, int)> build = [&](int p, int l, int r) {
      if (r - l == 1) {
        q[p] = Poly({1, -x[l]});
      } else {
        int m = (l + r) / 2;
        build(2 * p, l, m);
        build(2 * p + 1, m, r);
        q[p] = q[2 * p] * q[2 * p + 1];
      }
    };
    build(1, 0, n);
    std::function<void(int, int, int, const Poly &)> work =
        [&](int p, int l, int r, const Poly &num) {
          if (r - l == 1) {
            if (l < int(ans.size())) {
              ans[l] = num[0];
            }
          } else {
            int m = (l + r) / 2;
            work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
            work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
          }
        };
    work(1, 0, n, mulT(q[1].inv(n)));
    return ans;
  }
};
struct Matrix {
  Poly a[2][2];
};
Matrix mul(const Matrix &a, const Matrix &b, int n) {
  Matrix c;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      c.a[i][j] = (a.a[i][0] * b.a[0][j] + a.a[i][1] * b.a[1][j]).modxk(n + 1);
    }
  }
  return c;
}
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int n, m;
  std::cin >> n >> m;
  Matrix h, e;
  h.a[0][0] = Poly({1, P - 1});
  h.a[0][1] = Poly({0, 1});
  h.a[1][0] = Poly({P - 1});
  h.a[1][1] = Poly({1});
  e.a[0][0] = Poly({0, 1});
  e.a[1][0] = Poly({1});
  int N = (n + 1) / 2;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      h.a[i][j].resize(N + 1);
      e.a[i][j].resize(N + 1);
    }
  }
  for (int _ = m / 2; _; _ /= 2) {
    if (_ & 1) {
      e = mul(h, e, N);
    }
    h = mul(h, h, N);
  }
  auto f = (e.a[0][0] * e.a[1][0].inv(N + 1)).modxk(N + 1);
  f[1] = (m + 1) / 2;
  Poly g;
  g.resize(n + 1);
  for (int i = 1; i <= n; i += 2) {
    g[i] = f[(i + 1) / 2];
  }
  auto r = (Poly({1}) - g).inv(n + 1);
  for (int i = 1; i <= n; i += 2) {
    g[i] *= i;
  }
  r *= g;
  auto res = r[n];
  if (n % 2 == 0) {
    f = e.a[1][0].log(N + 1);
    res -= f[N] * n;
  }
  std::cout << res.val() << "\n";
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

XYMXYM and CQXYM will prepare n problems for Codeforces. The difficulty of the problem i will be an integer a_i, where a_i ≥ 0. The difficulty of the problems must satisfy a_i+a_{i+1}<m (1 ≤ i < n), and a_1+a_n<m, where m is a fixed integer. XYMXYM wants to know how many plans of the difficulty of the problems there are modulo 998 244 353.

Two plans of difficulty a and b are different only if there is an integer i (1 ≤ i ≤ n) satisfying a_i ≠ b_i.

Input

A single line contains two integers n and m (2 ≤ n ≤ 50 000, 1 ≤ m ≤ 10^9).

Output

Print a single integer — the number of different plans.

Examples

Input


3 2


Output


4


Input


5 9


Output


8105


Input


21038 3942834


Output


338529212

Note

In the first test case, the valid a are: [0,0,0], [0,0,1], [0,1,0], [1,0,0].

[1,0,1] is invalid since a_1+a_n ≥ m.

### Response

```cpp
#include <bits/stdc++.h>
constexpr int P = 998244353;
using i64 = long long;
int norm(int x) {
  if (x < 0) {
    x += P;
  }
  if (x >= P) {
    x -= P;
  }
  return x;
}
template <class T>
T power(T a, int b) {
  T res = 1;
  for (; b; b /= 2, a *= a) {
    if (b % 2) {
      res *= a;
    }
  }
  return res;
}
struct Z {
  int x;
  Z(int x = 0) : x(norm(x)) {}
  int val() const { return x; }
  Z operator-() const { return Z(norm(P - x)); }
  Z inv() const {
    assert(x != 0);
    return power(*this, P - 2);
  }
  Z &operator*=(const Z &rhs) {
    x = i64(x) * rhs.x % P;
    return *this;
  }
  Z &operator+=(const Z &rhs) {
    x = norm(x + rhs.x);
    return *this;
  }
  Z &operator-=(const Z &rhs) {
    x = norm(x - rhs.x);
    return *this;
  }
  Z &operator/=(const Z &rhs) { return *this *= rhs.inv(); }
  friend Z operator*(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res *= rhs;
    return res;
  }
  friend Z operator+(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res += rhs;
    return res;
  }
  friend Z operator-(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res -= rhs;
    return res;
  }
  friend Z operator/(const Z &lhs, const Z &rhs) {
    Z res = lhs;
    res /= rhs;
    return res;
  }
};
std::vector<int> rev;
std::vector<Z> roots{0, 1};
void dft(std::vector<Z> &a) {
  int n = a.size();
  if (int(rev.size()) != n) {
    int k = __builtin_ctz(n) - 1;
    rev.resize(n);
    for (int i = 0; i < n; i++) {
      rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
    }
  }
  for (int i = 0; i < n; i++) {
    if (rev[i] < i) {
      std::swap(a[i], a[rev[i]]);
    }
  }
  if (int(roots.size()) < n) {
    int k = __builtin_ctz(roots.size());
    roots.resize(n);
    while ((1 << k) < n) {
      Z e = power(Z(3), (P - 1) >> (k + 1));
      for (int i = 1 << (k - 1); i < (1 << k); i++) {
        roots[2 * i] = roots[i];
        roots[2 * i + 1] = roots[i] * e;
      }
      k++;
    }
  }
  for (int k = 1; k < n; k *= 2) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        Z u = a[i + j];
        Z v = a[i + j + k] * roots[k + j];
        a[i + j] = u + v;
        a[i + j + k] = u - v;
      }
    }
  }
}
void idft(std::vector<Z> &a) {
  int n = a.size();
  std::reverse(a.begin() + 1, a.end());
  dft(a);
  Z inv = Z(n).inv();
  for (int i = 0; i < n; i++) {
    a[i] *= inv;
  }
}
struct Poly {
  std::vector<Z> a;
  Poly() {}
  Poly(const std::vector<Z> &a) : a(a) {}
  int size() const { return a.size(); }
  void resize(int n) { a.resize(n); }
  Z operator[](int idx) const {
    if (idx < 0 || idx >= size()) {
      return 0;
    }
    return a[idx];
  }
  Z &operator[](int idx) { return a[idx]; }
  Poly mulxk(int k) const {
    auto b = a;
    b.insert(b.begin(), k, 0);
    return Poly(b);
  }
  Poly modxk(int k) const {
    k = std::min(k, size());
    return Poly(std::vector<Z>(a.begin(), a.begin() + k));
  }
  Poly divxk(int k) const {
    if (size() <= k) {
      return Poly();
    }
    return Poly(std::vector<Z>(a.begin() + k, a.end()));
  }
  friend Poly operator+(const Poly &a, const Poly &b) {
    std::vector<Z> res(std::max(a.size(), b.size()));
    for (int i = 0; i < int(res.size()); i++) {
      res[i] = a[i] + b[i];
    }
    return Poly(res);
  }
  friend Poly operator-(const Poly &a, const Poly &b) {
    std::vector<Z> res(std::max(a.size(), b.size()));
    for (int i = 0; i < int(res.size()); i++) {
      res[i] = a[i] - b[i];
    }
    return Poly(res);
  }
  friend Poly operator*(Poly a, Poly b) {
    if (a.size() == 0 || b.size() == 0) {
      return Poly();
    }
    int sz = 1, tot = a.size() + b.size() - 1;
    while (sz < tot) sz *= 2;
    a.a.resize(sz);
    b.a.resize(sz);
    dft(a.a);
    dft(b.a);
    for (int i = 0; i < sz; ++i) {
      a.a[i] = a[i] * b[i];
    }
    idft(a.a);
    a.resize(tot);
    return a;
  }
  friend Poly operator*(Z a, Poly b) {
    for (int i = 0; i < int(b.size()); i++) {
      b[i] *= a;
    }
    return b;
  }
  friend Poly operator*(Poly a, Z b) {
    for (int i = 0; i < int(a.size()); i++) {
      a[i] *= b;
    }
    return a;
  }
  Poly &operator+=(Poly b) { return (*this) = (*this) + b; }
  Poly &operator-=(Poly b) { return (*this) = (*this) - b; }
  Poly &operator*=(Poly b) { return (*this) = (*this) * b; }
  Poly deriv() const {
    if (a.empty()) {
      return Poly();
    }
    std::vector<Z> res(size() - 1);
    for (int i = 0; i < size() - 1; ++i) {
      res[i] = (i + 1) * a[i + 1];
    }
    return Poly(res);
  }
  Poly integr() const {
    std::vector<Z> res(size() + 1);
    for (int i = 0; i < size(); ++i) {
      res[i + 1] = a[i] / (i + 1);
    }
    return Poly(res);
  }
  Poly inv(int m) const {
    Poly x({a[0].inv()});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x * (Poly({2}) - modxk(k) * x)).modxk(k);
    }
    return x.modxk(m);
  }
  Poly log(int m) const { return (deriv() * inv(m)).integr().modxk(m); }
  Poly exp(int m) const {
    Poly x({1});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x * (Poly({1}) - x.log(k) + modxk(k))).modxk(k);
    }
    return x.modxk(m);
  }
  Poly sqrt(int m) const {
    Poly x({1});
    int k = 1;
    while (k < m) {
      k *= 2;
      x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
    }
    return x.modxk(m);
  }
  Poly mulT(Poly b) const {
    if (b.size() == 0) {
      return Poly();
    }
    int n = b.size();
    std::reverse(b.a.begin(), b.a.end());
    return ((*this) * b).divxk(n - 1);
  }
  std::vector<Z> eval(std::vector<Z> x) const {
    if (size() == 0) {
      return std::vector<Z>(x.size(), 0);
    }
    const int n = std::max(int(x.size()), size());
    std::vector<Poly> q(4 * n);
    std::vector<Z> ans(x.size());
    x.resize(n);
    std::function<void(int, int, int)> build = [&](int p, int l, int r) {
      if (r - l == 1) {
        q[p] = Poly({1, -x[l]});
      } else {
        int m = (l + r) / 2;
        build(2 * p, l, m);
        build(2 * p + 1, m, r);
        q[p] = q[2 * p] * q[2 * p + 1];
      }
    };
    build(1, 0, n);
    std::function<void(int, int, int, const Poly &)> work =
        [&](int p, int l, int r, const Poly &num) {
          if (r - l == 1) {
            if (l < int(ans.size())) {
              ans[l] = num[0];
            }
          } else {
            int m = (l + r) / 2;
            work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
            work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
          }
        };
    work(1, 0, n, mulT(q[1].inv(n)));
    return ans;
  }
};
struct Matrix {
  Poly a[2][2];
};
Matrix mul(const Matrix &a, const Matrix &b, int n) {
  Matrix c;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      c.a[i][j] = (a.a[i][0] * b.a[0][j] + a.a[i][1] * b.a[1][j]).modxk(n + 1);
    }
  }
  return c;
}
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int n, m;
  std::cin >> n >> m;
  Matrix h, e;
  h.a[0][0] = Poly({1, P - 1});
  h.a[0][1] = Poly({0, 1});
  h.a[1][0] = Poly({P - 1});
  h.a[1][1] = Poly({1});
  e.a[0][0] = Poly({0, 1});
  e.a[1][0] = Poly({1});
  int N = (n + 1) / 2;
  for (int i = 0; i < 2; i++) {
    for (int j = 0; j < 2; j++) {
      h.a[i][j].resize(N + 1);
      e.a[i][j].resize(N + 1);
    }
  }
  for (int _ = m / 2; _; _ /= 2) {
    if (_ & 1) {
      e = mul(h, e, N);
    }
    h = mul(h, h, N);
  }
  auto f = (e.a[0][0] * e.a[1][0].inv(N + 1)).modxk(N + 1);
  f[1] = (m + 1) / 2;
  Poly g;
  g.resize(n + 1);
  for (int i = 1; i <= n; i += 2) {
    g[i] = f[(i + 1) / 2];
  }
  auto r = (Poly({1}) - g).inv(n + 1);
  for (int i = 1; i <= n; i += 2) {
    g[i] *= i;
  }
  r *= g;
  auto res = r[n];
  if (n % 2 == 0) {
    f = e.a[1][0].log(N + 1);
    res -= f[N] * n;
  }
  std::cout << res.val() << "\n";
  return 0;
}

```