#include <bits/stdc++.h>
using namespace std;
template <class T>
void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
static void redirect(int argc, const char **argv) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  if (argc > 1) {
    static filebuf f;
    f.open(argv[1], ios::in);
    cin.rdbuf(&f);
    if (!cin) {
      cerr << "Failed to open '" << argv[1] << "'" << endl;
      exit(1);
    }
  }
  if (argc > 2) {
    static filebuf f;
    f.open(argv[2], ios::out | ios::trunc);
    cout.rdbuf(&f);
    if (!cout) {
      cerr << "Failed to open '" << argv[2] << "'" << endl;
    }
  }
  cin.exceptions(ios::failbit);
}
template <typename T>
static constexpr T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <typename T>
static constexpr T wrap_pos(T a, T m) {
  return a < 0 ? a + m : a;
}
template <typename T>
static constexpr T sqr(T a) {
  return a * a;
}
template <typename T>
static constexpr T mod(T a, T m) {
  return wrap_pos(a % m, m);
}
template <typename T>
static constexpr T inverse2(T a, T m) {
  return a <= 1 ? a : mod((1 - inverse2(m % a, a) * m) / a, m);
}
template <typename T>
static constexpr T inverse(T a, T m) {
  return inverse2(mod(a, m), m);
}
template <typename T, typename P>
static constexpr T power(T a, P b) {
  return b == 0 ? T(1) : (b % 2) ? power(a, b - 1) * a : sqr(power(a, b / 2));
}
template <typename T, typename C, T Modulus>
class MR {
 private:
  struct tag_plus {};
  struct tag_minus {};
  struct tag_good {};
  T value;
  static_assert(std::numeric_limits<C>::max() / Modulus / Modulus > 0,
                "compute type is too small");
  static_assert(Modulus < std::numeric_limits<T>::max() / 2,
                "storage type is too small");
  static constexpr T reduce(T value, tag_plus) {
    return value >= Modulus ? value - Modulus : value;
  }
  static constexpr T reduce(T value, tag_minus) {
    return value < 0 ? value + Modulus : value;
  }
  static constexpr T reduce(T value, tag_good) { return value; }

 public:
  static constexpr T modulus = Modulus;
  constexpr MR() : value(0) {}
  constexpr MR(C value) : value(reduce(value % Modulus, tag_minus())) {}
  template <typename tag_t>
  constexpr MR(T value, tag_t tag) : value(reduce(value, tag)) {}
  MR &operator=(C value) {
    this->value = reduce(value % Modulus, tag_minus());
    return *this;
  }
  constexpr MR operator+(MR b) const { return MR(value + b.value, tag_plus()); }
  constexpr MR operator-(MR b) const {
    return MR(value - b.value, tag_minus());
  }
  constexpr MR operator*(MR b) const {
    return MR(C(value) * C(b.value) % Modulus, tag_good());
  }
  constexpr MR operator-() const { return MR(-value, tag_minus()); }
  MR &operator+=(MR b) {
    value = reduce(value + b.value, tag_plus());
    return *this;
  }
  MR &operator-=(MR b) {
    value = reduce(value - b.value, tag_minus());
    return *this;
  }
  MR &operator*=(MR b) {
    value = C(value) * C(b.value) % Modulus;
    return *this;
  }
  constexpr bool operator==(MR b) const { return value == b.value; }
  constexpr bool operator!=(MR b) const { return value != b.value; }
  constexpr T get() const { return value; }
  constexpr MR inverse() const {
    return MR(::inverse(C(value), C(Modulus)), tag_good());
  }
  constexpr MR operator/(MR b) const { return *this * b.inverse(); }
  MR &operator/=(MR b) { return *this *= b.inverse(); }
};
template <typename T, typename C, T Modulus>
static inline std::ostream &operator<<(std::ostream &o, MR<T, C, Modulus> mr) {
  return o << mr.get();
}
int main(int argc, const char **argv) {
  redirect(argc, argv);
  int N, M, K;
  cin >> N >> M >> K;
  MR<int, long long, 998244353> iM = MR<int, long long, 998244353>(M).inverse();
  vector<MR<int, long long, 998244353>> iMp(K + 1);
  iMp[0] = 1;
  for (int i = 1; i <= K; i++) iMp[i] = iMp[i - 1] * iM;
  vector<vector<MR<int, long long, 998244353>>> choose(
      K + 1, vector<MR<int, long long, 998244353>>(K + 1));
  for (int i = 0; i <= K; i++) {
    choose[i][0] = choose[i][i] = 1;
    for (int j = 1; j < i; j++)
      choose[i][j] = choose[i - 1][j] + choose[i - 1][j - 1];
  }
  vector<MR<int, long long, 998244353>> inv(K + 1);
  for (int i = 1; i <= K; i++)
    inv[i] = MR<int, long long, 998244353>(i).inverse();
  vector<MR<int, long long, 998244353>> ways(K + 1);
  MR<int, long long, 998244353> nci = 1;
  MR<int, long long, 998244353> ans = 0;
  for (int i = 1; i <= min(N, K); i++) {
    nci = nci * MR<int, long long, 998244353>(N - i + 1) * inv[i];
    MR<int, long long, 998244353> w =
        nci * power(MR<int, long long, 998244353>(i), K);
    MR<int, long long, 998244353> scale = 1;
    for (int j = i - 1; j > 0; j--) {
      scale = scale * MR<int, long long, 998244353>(N - j) * inv[i - j];
      w -= ways[j] * scale;
    }
    ways[i] = w;
    ans += w * iMp[i];
  }
  cout << ans << '\n';
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

Consider the following experiment. You have a deck of m cards, and exactly one card is a joker. n times, you do the following: shuffle the deck, take the top card of the deck, look at it and return it into the deck.

Let x be the number of times you have taken the joker out of the deck during this experiment. Assuming that every time you shuffle the deck, all m! possible permutations of cards are equiprobable, what is the expected value of x^k? Print the answer modulo 998244353.

Input

The only line contains three integers n, m and k (1 ≤ n, m < 998244353, 1 ≤ k ≤ 5000).

Output

Print one integer — the expected value of x^k, taken modulo 998244353 (the answer can always be represented as an irreducible fraction a/b, where b mod 998244353 ≠ 0; you have to print a ⋅ b^{-1} mod 998244353).

Examples

Input


1 1 1


Output


1


Input


1 1 5000


Output


1


Input


2 2 2


Output


499122178


Input


998244352 1337 5000


Output


326459680

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
void splitstr(const string &s, vector<T> &out) {
  istringstream in(s);
  out.clear();
  copy(istream_iterator<T>(in), istream_iterator<T>(), back_inserter(out));
}
static void redirect(int argc, const char **argv) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  if (argc > 1) {
    static filebuf f;
    f.open(argv[1], ios::in);
    cin.rdbuf(&f);
    if (!cin) {
      cerr << "Failed to open '" << argv[1] << "'" << endl;
      exit(1);
    }
  }
  if (argc > 2) {
    static filebuf f;
    f.open(argv[2], ios::out | ios::trunc);
    cout.rdbuf(&f);
    if (!cout) {
      cerr << "Failed to open '" << argv[2] << "'" << endl;
    }
  }
  cin.exceptions(ios::failbit);
}
template <typename T>
static constexpr T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <typename T>
static constexpr T wrap_pos(T a, T m) {
  return a < 0 ? a + m : a;
}
template <typename T>
static constexpr T sqr(T a) {
  return a * a;
}
template <typename T>
static constexpr T mod(T a, T m) {
  return wrap_pos(a % m, m);
}
template <typename T>
static constexpr T inverse2(T a, T m) {
  return a <= 1 ? a : mod((1 - inverse2(m % a, a) * m) / a, m);
}
template <typename T>
static constexpr T inverse(T a, T m) {
  return inverse2(mod(a, m), m);
}
template <typename T, typename P>
static constexpr T power(T a, P b) {
  return b == 0 ? T(1) : (b % 2) ? power(a, b - 1) * a : sqr(power(a, b / 2));
}
template <typename T, typename C, T Modulus>
class MR {
 private:
  struct tag_plus {};
  struct tag_minus {};
  struct tag_good {};
  T value;
  static_assert(std::numeric_limits<C>::max() / Modulus / Modulus > 0,
                "compute type is too small");
  static_assert(Modulus < std::numeric_limits<T>::max() / 2,
                "storage type is too small");
  static constexpr T reduce(T value, tag_plus) {
    return value >= Modulus ? value - Modulus : value;
  }
  static constexpr T reduce(T value, tag_minus) {
    return value < 0 ? value + Modulus : value;
  }
  static constexpr T reduce(T value, tag_good) { return value; }

 public:
  static constexpr T modulus = Modulus;
  constexpr MR() : value(0) {}
  constexpr MR(C value) : value(reduce(value % Modulus, tag_minus())) {}
  template <typename tag_t>
  constexpr MR(T value, tag_t tag) : value(reduce(value, tag)) {}
  MR &operator=(C value) {
    this->value = reduce(value % Modulus, tag_minus());
    return *this;
  }
  constexpr MR operator+(MR b) const { return MR(value + b.value, tag_plus()); }
  constexpr MR operator-(MR b) const {
    return MR(value - b.value, tag_minus());
  }
  constexpr MR operator*(MR b) const {
    return MR(C(value) * C(b.value) % Modulus, tag_good());
  }
  constexpr MR operator-() const { return MR(-value, tag_minus()); }
  MR &operator+=(MR b) {
    value = reduce(value + b.value, tag_plus());
    return *this;
  }
  MR &operator-=(MR b) {
    value = reduce(value - b.value, tag_minus());
    return *this;
  }
  MR &operator*=(MR b) {
    value = C(value) * C(b.value) % Modulus;
    return *this;
  }
  constexpr bool operator==(MR b) const { return value == b.value; }
  constexpr bool operator!=(MR b) const { return value != b.value; }
  constexpr T get() const { return value; }
  constexpr MR inverse() const {
    return MR(::inverse(C(value), C(Modulus)), tag_good());
  }
  constexpr MR operator/(MR b) const { return *this * b.inverse(); }
  MR &operator/=(MR b) { return *this *= b.inverse(); }
};
template <typename T, typename C, T Modulus>
static inline std::ostream &operator<<(std::ostream &o, MR<T, C, Modulus> mr) {
  return o << mr.get();
}
int main(int argc, const char **argv) {
  redirect(argc, argv);
  int N, M, K;
  cin >> N >> M >> K;
  MR<int, long long, 998244353> iM = MR<int, long long, 998244353>(M).inverse();
  vector<MR<int, long long, 998244353>> iMp(K + 1);
  iMp[0] = 1;
  for (int i = 1; i <= K; i++) iMp[i] = iMp[i - 1] * iM;
  vector<vector<MR<int, long long, 998244353>>> choose(
      K + 1, vector<MR<int, long long, 998244353>>(K + 1));
  for (int i = 0; i <= K; i++) {
    choose[i][0] = choose[i][i] = 1;
    for (int j = 1; j < i; j++)
      choose[i][j] = choose[i - 1][j] + choose[i - 1][j - 1];
  }
  vector<MR<int, long long, 998244353>> inv(K + 1);
  for (int i = 1; i <= K; i++)
    inv[i] = MR<int, long long, 998244353>(i).inverse();
  vector<MR<int, long long, 998244353>> ways(K + 1);
  MR<int, long long, 998244353> nci = 1;
  MR<int, long long, 998244353> ans = 0;
  for (int i = 1; i <= min(N, K); i++) {
    nci = nci * MR<int, long long, 998244353>(N - i + 1) * inv[i];
    MR<int, long long, 998244353> w =
        nci * power(MR<int, long long, 998244353>(i), K);
    MR<int, long long, 998244353> scale = 1;
    for (int j = i - 1; j > 0; j--) {
      scale = scale * MR<int, long long, 998244353>(N - j) * inv[i - j];
      w -= ways[j] * scale;
    }
    ways[i] = w;
    ans += w * iMp[i];
  }
  cout << ans << '\n';
  return 0;
}

```