#include <bits/stdc++.h>
using namespace std;
constexpr int inf = 1 << 30;
constexpr long long llinf = 1LL << 62;
constexpr int mod = 998244353;
constexpr int dy[4] = {-1, 0, 1, 0}, dx[4] = {0, -1, 0, 1};
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
inline int popcount(ll x) { return __builtin_popcountll(x); }
inline int div2num(ll x) { return __builtin_ctzll(x); }
inline bool bit(ll x, int b) { return (x >> b) & 1; }
template <class T>
bool chmax(T& a, const T& b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
string to_string(T s);
template <class S, class T>
string to_string(pair<S, T> p);
string to_string(char c) { return string(1, c); }
string to_string(string s) { return s; }
string to_string(const char s[]) { return string(s); }
template <class T>
string to_string(T v) {
  if (v.empty()) return "{}";
  string ret = "{";
  for (auto x : v) ret += to_string(x) + ",";
  ret.back() = '}';
  return ret;
}
template <class S, class T>
string to_string(pair<S, T> p) {
  return "{" + to_string(p.first) + ":" + to_string(p.second) + "}";
}
void debug() { cerr << endl; }
template <class Head, class... Tail>
void debug(Head head, Tail... tail) {
  cerr << to_string(head) << " ";
  debug(tail...);
}
template <class T>
vector<T> makev(int n, T v) {
  return vector<T>(n, v);
}
struct IO {
  std::string separator = " ";
  template <class T>
  inline void read(T& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c != '-' && (c < '0' || '9' < c));
    bool minus = 0;
    if (c == '-') {
      minus = 1;
      c = getchar_unlocked();
    }
    x = 0;
    while ('0' <= c && c <= '9') {
      x *= 10;
      x += c - '0';
      c = getchar_unlocked();
    }
    if (minus) x = -x;
  }
  inline void read(std::string& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c == ' ' || c == '\n');
    x.clear();
    do {
      x += c;
      c = getchar_unlocked();
    } while (c != ' ' && c != '\n' && c != EOF);
  }
  template <class T>
  inline void read(std::vector<T>& v) {
    for (auto& x : v) read(x);
  }
  template <class S, class T>
  inline void read(std::pair<S, T>& p) {
    read(p.first);
    read(p.second);
  }
  template <class Head, class... Tail>
  inline void read(Head& head, Tail&... tail) {
    read(head);
    read(tail...);
  }
  template <class T>
  inline void write(T x) {
    char buf[32];
    int p = 0;
    if (x < 0) {
      x = -x;
      putchar_unlocked('-');
    }
    if (x == 0) putchar_unlocked('0');
    while (x > 0) {
      buf[p++] = (x % 10) + '0';
      x /= 10;
    }
    while (p) {
      putchar_unlocked(buf[--p]);
    }
  }
  inline void write(std::string x) {
    for (char c : x) putchar_unlocked(c);
  }
  inline void write(const char s[]) {
    for (int i = 0; s[i] != 0; ++i) putchar_unlocked(s[i]);
  }
  template <class T>
  inline void write(std::vector<T> v) {
    if (v.empty()) return;
    for (auto itr = v.begin(); itr + 1 != v.end(); ++itr) {
      write(*itr);
      write(separator);
    }
    write(v.back());
  }
  template <class Head, class... Tail>
  inline void write(Head head, Tail... tail) {
    write(head);
    write(separator);
    write(tail...);
  }
  template <class Head, class... Tail>
  inline void writeln(Head head, Tail... tail) {
    write(head, tail...);
    write("\n");
  }
  void set_separator(std::string s) { separator = s; }
} io;
struct Prime {
  int n;
  vector<int> table;
  vector<int> primes;
  Prime(int _n = 100000) {
    n = _n + 1;
    table.resize(n, -1);
    table[0] = 0;
    table[1] = -1;
    for (int i = 2; i * i < n; ++i) {
      if (table[i] == -1) {
        for (int j = i * i; j < n; j += i) {
          table[j] = i;
        }
      }
    }
  }
  void enumerate_primes() {
    primes.clear();
    for (int i = 2; i < n; ++i) {
      if (table[i] == -1) primes.push_back(i);
    }
  }
  vector<pair<long long, int>> prime_factor(long long x) {
    map<long long, int> mp;
    long long div = 2;
    int p = 0;
    while (n <= x && div * div <= x) {
      if (x % div == 0) {
        mp[div]++;
        x /= div;
      } else {
        if (p + 1 < primes.size()) {
          div = primes[++p];
        } else {
          div++;
        }
      }
    }
    if (x < n) {
      while (table[x] != -1) {
        mp[table[x]]++;
        x /= table[x];
      }
    }
    if (x > 1) mp[x]++;
    vector<pair<long long, int>> ret;
    for (auto p : mp) ret.push_back(p);
    return ret;
  }
};
template <int MOD = 1000000007>
struct Math {
  vector<long long> fact, factinv, inv;
  Math(int n = 100000) {
    fact.resize(n + 1);
    factinv.resize(n + 1);
    inv.resize(n + 1);
    fact[0] = fact[1] = 1;
    factinv[0] = factinv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i <= n; ++i) {
      fact[i] = fact[i - 1] * i % MOD;
      inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
      factinv[i] = factinv[i - 1] * inv[i] % MOD;
    }
  }
  long long C(int n, int r) {
    if (n < r || n < 0 || r < 0) {
      return 0;
    } else {
      return fact[n] * (factinv[r] * factinv[n - r] % MOD) % MOD;
    }
  }
  long long P(int n, int r) {
    if (n < r || n < 0 || r < 0) {
      return 0;
    } else {
      return fact[n] * factinv[n - r] % MOD;
    }
  }
  long long H(int n, int r) { return C(n + r - 1, r); }
};
struct UnionFind {
  vector<int> data;
  vector<vector<int>> groups;
  UnionFind(int n) : data(n, -1) {}
  int root(int v) { return data[v] < 0 ? v : data[v] = root(data[v]); }
  bool unite(int u, int v) {
    if ((u = root(u)) == (v = root(v))) {
      return 1;
    } else {
      if (-data[u] < -data[v]) swap(u, v);
      data[u] += data[v];
      data[v] = u;
      return 0;
    }
  }
  int size(int v) { return -data[root(v)]; }
  void make_groups() {
    map<int, vector<int>> mp;
    for (int i = 0; i < data.size(); ++i) mp[root(i)].push_back(i);
    groups.clear();
    for (auto p : mp) groups.push_back(p.second);
  }
};
namespace phc {
long long modpow(long long a, long long n) {
  long long res = 1;
  while (n > 0) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}
long long modinv(long long a) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
long long gcd(long long a, long long b) { return b != 0 ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
}  // namespace phc
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; }
  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>;
int main() {
  int n, x;
  io.read(n, x);
  Math<mod> math(n + x);
  vector<vector<modint>> dp(n + 1, vector<modint>(x + 1)),
      pows(n + x + 1, vector<modint>(n + x + 1, 1));
  dp[0][0] = 1;
  for (int i = 0; i < (int)n + x + 1; i++)
    for (int j = 1; j < (int)n + x + 1; j++) pows[i][j] = pows[i][j - 1] * i;
  modint ans = 0;
  for (int i = 0; i < (int)n; i++) {
    for (int j = 0; j < (int)x; j++)
      if (dp[i][j].x > 0) {
        int use = n - i - 1;
        for (int k = i; k <= n; ++k) {
          dp[k][min(x, j + use)] +=
              dp[i][j] * pows[min(use, x - j)][k - i] * math.C(n - i, k - i);
          if (i + 1 < n && k == n) {
            ans +=
                dp[i][j] * pows[min(use, x - j)][k - i] * math.C(n - i, k - i);
          }
        }
      }
  }
  io.writeln(ans.x);
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

There are n heroes fighting in the arena. Initially, the i-th hero has a_i health points.

The fight in the arena takes place in several rounds. At the beginning of each round, each alive hero deals 1 damage to all other heroes. Hits of all heroes occur simultaneously. Heroes whose health is less than 1 at the end of the round are considered killed.

If exactly 1 hero remains alive after a certain round, then he is declared the winner. Otherwise, there is no winner.

Your task is to calculate the number of ways to choose the initial health points for each hero a_i, where 1 ≤ a_i ≤ x, so that there is no winner of the fight. The number of ways can be very large, so print it modulo 998244353. Two ways are considered different if at least one hero has a different amount of health. For example, [1, 2, 1] and [2, 1, 1] are different.

Input

The only line contains two integers n and x (2 ≤ n ≤ 500; 1 ≤ x ≤ 500).

Output

Print one integer — the number of ways to choose the initial health points for each hero a_i, where 1 ≤ a_i ≤ x, so that there is no winner of the fight, taken modulo 998244353. 

Examples

Input


2 5


Output


5


Input


3 3


Output


15


Input


5 4


Output


1024


Input


13 37


Output


976890680

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
constexpr int inf = 1 << 30;
constexpr long long llinf = 1LL << 62;
constexpr int mod = 998244353;
constexpr int dy[4] = {-1, 0, 1, 0}, dx[4] = {0, -1, 0, 1};
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
inline int popcount(ll x) { return __builtin_popcountll(x); }
inline int div2num(ll x) { return __builtin_ctzll(x); }
inline bool bit(ll x, int b) { return (x >> b) & 1; }
template <class T>
bool chmax(T& a, const T& b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
string to_string(T s);
template <class S, class T>
string to_string(pair<S, T> p);
string to_string(char c) { return string(1, c); }
string to_string(string s) { return s; }
string to_string(const char s[]) { return string(s); }
template <class T>
string to_string(T v) {
  if (v.empty()) return "{}";
  string ret = "{";
  for (auto x : v) ret += to_string(x) + ",";
  ret.back() = '}';
  return ret;
}
template <class S, class T>
string to_string(pair<S, T> p) {
  return "{" + to_string(p.first) + ":" + to_string(p.second) + "}";
}
void debug() { cerr << endl; }
template <class Head, class... Tail>
void debug(Head head, Tail... tail) {
  cerr << to_string(head) << " ";
  debug(tail...);
}
template <class T>
vector<T> makev(int n, T v) {
  return vector<T>(n, v);
}
struct IO {
  std::string separator = " ";
  template <class T>
  inline void read(T& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c != '-' && (c < '0' || '9' < c));
    bool minus = 0;
    if (c == '-') {
      minus = 1;
      c = getchar_unlocked();
    }
    x = 0;
    while ('0' <= c && c <= '9') {
      x *= 10;
      x += c - '0';
      c = getchar_unlocked();
    }
    if (minus) x = -x;
  }
  inline void read(std::string& x) {
    char c;
    do {
      c = getchar_unlocked();
    } while (c == ' ' || c == '\n');
    x.clear();
    do {
      x += c;
      c = getchar_unlocked();
    } while (c != ' ' && c != '\n' && c != EOF);
  }
  template <class T>
  inline void read(std::vector<T>& v) {
    for (auto& x : v) read(x);
  }
  template <class S, class T>
  inline void read(std::pair<S, T>& p) {
    read(p.first);
    read(p.second);
  }
  template <class Head, class... Tail>
  inline void read(Head& head, Tail&... tail) {
    read(head);
    read(tail...);
  }
  template <class T>
  inline void write(T x) {
    char buf[32];
    int p = 0;
    if (x < 0) {
      x = -x;
      putchar_unlocked('-');
    }
    if (x == 0) putchar_unlocked('0');
    while (x > 0) {
      buf[p++] = (x % 10) + '0';
      x /= 10;
    }
    while (p) {
      putchar_unlocked(buf[--p]);
    }
  }
  inline void write(std::string x) {
    for (char c : x) putchar_unlocked(c);
  }
  inline void write(const char s[]) {
    for (int i = 0; s[i] != 0; ++i) putchar_unlocked(s[i]);
  }
  template <class T>
  inline void write(std::vector<T> v) {
    if (v.empty()) return;
    for (auto itr = v.begin(); itr + 1 != v.end(); ++itr) {
      write(*itr);
      write(separator);
    }
    write(v.back());
  }
  template <class Head, class... Tail>
  inline void write(Head head, Tail... tail) {
    write(head);
    write(separator);
    write(tail...);
  }
  template <class Head, class... Tail>
  inline void writeln(Head head, Tail... tail) {
    write(head, tail...);
    write("\n");
  }
  void set_separator(std::string s) { separator = s; }
} io;
struct Prime {
  int n;
  vector<int> table;
  vector<int> primes;
  Prime(int _n = 100000) {
    n = _n + 1;
    table.resize(n, -1);
    table[0] = 0;
    table[1] = -1;
    for (int i = 2; i * i < n; ++i) {
      if (table[i] == -1) {
        for (int j = i * i; j < n; j += i) {
          table[j] = i;
        }
      }
    }
  }
  void enumerate_primes() {
    primes.clear();
    for (int i = 2; i < n; ++i) {
      if (table[i] == -1) primes.push_back(i);
    }
  }
  vector<pair<long long, int>> prime_factor(long long x) {
    map<long long, int> mp;
    long long div = 2;
    int p = 0;
    while (n <= x && div * div <= x) {
      if (x % div == 0) {
        mp[div]++;
        x /= div;
      } else {
        if (p + 1 < primes.size()) {
          div = primes[++p];
        } else {
          div++;
        }
      }
    }
    if (x < n) {
      while (table[x] != -1) {
        mp[table[x]]++;
        x /= table[x];
      }
    }
    if (x > 1) mp[x]++;
    vector<pair<long long, int>> ret;
    for (auto p : mp) ret.push_back(p);
    return ret;
  }
};
template <int MOD = 1000000007>
struct Math {
  vector<long long> fact, factinv, inv;
  Math(int n = 100000) {
    fact.resize(n + 1);
    factinv.resize(n + 1);
    inv.resize(n + 1);
    fact[0] = fact[1] = 1;
    factinv[0] = factinv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i <= n; ++i) {
      fact[i] = fact[i - 1] * i % MOD;
      inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
      factinv[i] = factinv[i - 1] * inv[i] % MOD;
    }
  }
  long long C(int n, int r) {
    if (n < r || n < 0 || r < 0) {
      return 0;
    } else {
      return fact[n] * (factinv[r] * factinv[n - r] % MOD) % MOD;
    }
  }
  long long P(int n, int r) {
    if (n < r || n < 0 || r < 0) {
      return 0;
    } else {
      return fact[n] * factinv[n - r] % MOD;
    }
  }
  long long H(int n, int r) { return C(n + r - 1, r); }
};
struct UnionFind {
  vector<int> data;
  vector<vector<int>> groups;
  UnionFind(int n) : data(n, -1) {}
  int root(int v) { return data[v] < 0 ? v : data[v] = root(data[v]); }
  bool unite(int u, int v) {
    if ((u = root(u)) == (v = root(v))) {
      return 1;
    } else {
      if (-data[u] < -data[v]) swap(u, v);
      data[u] += data[v];
      data[v] = u;
      return 0;
    }
  }
  int size(int v) { return -data[root(v)]; }
  void make_groups() {
    map<int, vector<int>> mp;
    for (int i = 0; i < data.size(); ++i) mp[root(i)].push_back(i);
    groups.clear();
    for (auto p : mp) groups.push_back(p.second);
  }
};
namespace phc {
long long modpow(long long a, long long n) {
  long long res = 1;
  while (n > 0) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}
long long modinv(long long a) {
  long long b = mod, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= mod;
  if (u < 0) u += mod;
  return u;
}
long long gcd(long long a, long long b) { return b != 0 ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
}  // namespace phc
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; }
  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>;
int main() {
  int n, x;
  io.read(n, x);
  Math<mod> math(n + x);
  vector<vector<modint>> dp(n + 1, vector<modint>(x + 1)),
      pows(n + x + 1, vector<modint>(n + x + 1, 1));
  dp[0][0] = 1;
  for (int i = 0; i < (int)n + x + 1; i++)
    for (int j = 1; j < (int)n + x + 1; j++) pows[i][j] = pows[i][j - 1] * i;
  modint ans = 0;
  for (int i = 0; i < (int)n; i++) {
    for (int j = 0; j < (int)x; j++)
      if (dp[i][j].x > 0) {
        int use = n - i - 1;
        for (int k = i; k <= n; ++k) {
          dp[k][min(x, j + use)] +=
              dp[i][j] * pows[min(use, x - j)][k - i] * math.C(n - i, k - i);
          if (i + 1 < n && k == n) {
            ans +=
                dp[i][j] * pows[min(use, x - j)][k - i] * math.C(n - i, k - i);
          }
        }
      }
  }
  io.writeln(ans.x);
  return 0;
}

```