#include <bits/stdc++.h>
template <typename T>
void MACRO_VAR_Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First& first, Rest&... rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
template <typename T>
void MACRO_VEC_ROW_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
template <class T>
inline T CHMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T>
inline T CHMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
template <class T>
using V = std::vector<T>;
template <class T>
using VV = V<V<T>>;
template <typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<ll, ll>;
using PAIRLL = std::pair<ll, ll>;
constexpr ll INFINT = (1 << 30) - 1;
constexpr ll INFINT_LIM = (1LL << 31) - 1;
constexpr ll INFLL = 1LL << 60;
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);
constexpr double EPS = 1e-10;
constexpr ll MOD = 998244353;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N>
void FILL(T (&a)[N], const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T& val) {
  for (auto& b : a) FILL(b, val);
}
template <class T>
void FILL(std::vector<T>& a, const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>>& a, const T& val) {
  for (auto& b : a) FILL(b, val);
}
class ModInt {
  friend std::istream& operator>>(std::istream& is, ModInt& obj);

 public:
  ll val;
  ModInt() : val(0) {}
  ModInt(ll n) : val(n % MOD) {
    if (val < 0) val += MOD;
  }
  ModInt& operator=(const ll& r) {
    val = r % MOD;
    if (r < 0) val += MOD;
    return *this;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const {
    ModInt res;
    res.val = (val) ? MOD - val : 0;
    return res;
  }
  ModInt& operator+=(const ModInt& r) {
    if ((val += r.val) >= MOD) val -= MOD;
    return *this;
  }
  ModInt& operator+=(const ll& r) { return *this += ModInt(r); }
  ModInt& operator-=(const ModInt& r) { return *this += -r; }
  ModInt& operator-=(const ll& r) { return *this -= ModInt(r); }
  ModInt& operator++() { return *this += 1; }
  ModInt& operator++(signed tmp) { return *this += 1; }
  ModInt& operator--() { return *this += MOD - 1; }
  ModInt& operator--(signed tmp) { return *this += MOD - 1; }
  ModInt& operator*=(const ModInt& r) {
    (val *= r.val) %= MOD;
    return *this;
  }
  ModInt& operator*=(const ll& r) { return *this *= ModInt(r); }
  ModInt& operator^=(ll p) {
    ModInt res(1);
    while (p) {
      if (p & 1) res *= *this;
      *this *= *this;
      p >>= 1;
    }
    return *this = res;
  }
  ModInt& operator/=(const ModInt& r) { return *this *= r ^ (MOD - 2); }
  ModInt& operator/=(const ll& r) { return *this /= ModInt(r); }
  ModInt operator+(const ModInt& r) const {
    auto res(*this);
    return res += r;
  }
  ModInt operator-(const ModInt& r) const {
    auto res(*this);
    return res -= r;
  }
  ModInt operator*(const ModInt& r) const {
    auto res(*this);
    return res *= r;
  }
  ModInt operator/(const ModInt& r) const {
    auto res(*this);
    return res /= r;
  }
  ModInt operator+(const ll& r) const {
    auto res(*this);
    return res += r;
  }
  ModInt operator-(const ll& r) const {
    auto res(*this);
    return res -= r;
  }
  ModInt operator*(const ll& r) const {
    auto res(*this);
    return res *= r;
  }
  ModInt operator^(const ll& r) const {
    auto res(*this);
    return res ^= r;
  }
  ModInt operator/(const ll& r) const {
    auto res(*this);
    return res /= r;
  }
};
std::ostream& operator<<(std::ostream& os, const ModInt& obj) {
  os << obj.val;
  return os;
}
std::istream& operator>>(std::istream& is, ModInt& obj) {
  is >> obj.val;
  obj.val %= MOD;
  if (obj.val < 0) obj.val += MOD;
  return is;
}
ModInt dp[5003][5003];
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  ll n, m, k;
  MACRO_VAR_Scan(n, m, k);
  ;
  {
    dp[0][0] = 1;
    for (ll p = 0; p < ll(k); ++p)
      for (ll c = 0; c < ll(k); ++c) {
        if (dp[p][c].val == 0) continue;
        dp[p + 1][c + 0] += dp[p][c] * c;
        dp[p + 1][c + 1] += dp[p][c] * (n - c);
      }
  }
  ModInt ans = 0;
  ModInt invM = 1;
  invM /= m;
  ModInt powInvM = 1;
  for (ll c = 0; c < ll(k + 1); ++c) {
    ans += dp[k][c] * powInvM;
    powInvM *= invM;
  }
  std::cout << (ans);
  std::cout << "\n";
  ;
  return 0;
}

### Prompt

Create a solution in Cpp for 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>
template <typename T>
void MACRO_VAR_Scan(T& t) {
  std::cin >> t;
}
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First& first, Rest&... rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
template <typename T>
void MACRO_VEC_ROW_Init(int n, T& t) {
  t.resize(n);
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First& first, Rest&... rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T>
void MACRO_VEC_ROW_Scan(int p, T& t) {
  std::cin >> t[p];
}
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First& first, Rest&... rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
template <class T>
inline T CHMAX(T& a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T>
inline T CHMIN(T& a, const T b) {
  return a = (a > b) ? b : a;
}
template <class T>
using V = std::vector<T>;
template <class T>
using VV = V<V<T>>;
template <typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<ll, ll>;
using PAIRLL = std::pair<ll, ll>;
constexpr ll INFINT = (1 << 30) - 1;
constexpr ll INFINT_LIM = (1LL << 31) - 1;
constexpr ll INFLL = 1LL << 60;
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);
constexpr double EPS = 1e-10;
constexpr ll MOD = 998244353;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N>
void FILL(T (&a)[N], const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T& val) {
  for (auto& b : a) FILL(b, val);
}
template <class T>
void FILL(std::vector<T>& a, const T& val) {
  for (auto& x : a) x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>>& a, const T& val) {
  for (auto& b : a) FILL(b, val);
}
class ModInt {
  friend std::istream& operator>>(std::istream& is, ModInt& obj);

 public:
  ll val;
  ModInt() : val(0) {}
  ModInt(ll n) : val(n % MOD) {
    if (val < 0) val += MOD;
  }
  ModInt& operator=(const ll& r) {
    val = r % MOD;
    if (r < 0) val += MOD;
    return *this;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const {
    ModInt res;
    res.val = (val) ? MOD - val : 0;
    return res;
  }
  ModInt& operator+=(const ModInt& r) {
    if ((val += r.val) >= MOD) val -= MOD;
    return *this;
  }
  ModInt& operator+=(const ll& r) { return *this += ModInt(r); }
  ModInt& operator-=(const ModInt& r) { return *this += -r; }
  ModInt& operator-=(const ll& r) { return *this -= ModInt(r); }
  ModInt& operator++() { return *this += 1; }
  ModInt& operator++(signed tmp) { return *this += 1; }
  ModInt& operator--() { return *this += MOD - 1; }
  ModInt& operator--(signed tmp) { return *this += MOD - 1; }
  ModInt& operator*=(const ModInt& r) {
    (val *= r.val) %= MOD;
    return *this;
  }
  ModInt& operator*=(const ll& r) { return *this *= ModInt(r); }
  ModInt& operator^=(ll p) {
    ModInt res(1);
    while (p) {
      if (p & 1) res *= *this;
      *this *= *this;
      p >>= 1;
    }
    return *this = res;
  }
  ModInt& operator/=(const ModInt& r) { return *this *= r ^ (MOD - 2); }
  ModInt& operator/=(const ll& r) { return *this /= ModInt(r); }
  ModInt operator+(const ModInt& r) const {
    auto res(*this);
    return res += r;
  }
  ModInt operator-(const ModInt& r) const {
    auto res(*this);
    return res -= r;
  }
  ModInt operator*(const ModInt& r) const {
    auto res(*this);
    return res *= r;
  }
  ModInt operator/(const ModInt& r) const {
    auto res(*this);
    return res /= r;
  }
  ModInt operator+(const ll& r) const {
    auto res(*this);
    return res += r;
  }
  ModInt operator-(const ll& r) const {
    auto res(*this);
    return res -= r;
  }
  ModInt operator*(const ll& r) const {
    auto res(*this);
    return res *= r;
  }
  ModInt operator^(const ll& r) const {
    auto res(*this);
    return res ^= r;
  }
  ModInt operator/(const ll& r) const {
    auto res(*this);
    return res /= r;
  }
};
std::ostream& operator<<(std::ostream& os, const ModInt& obj) {
  os << obj.val;
  return os;
}
std::istream& operator>>(std::istream& is, ModInt& obj) {
  is >> obj.val;
  obj.val %= MOD;
  if (obj.val < 0) obj.val += MOD;
  return is;
}
ModInt dp[5003][5003];
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  ;
  ll n, m, k;
  MACRO_VAR_Scan(n, m, k);
  ;
  {
    dp[0][0] = 1;
    for (ll p = 0; p < ll(k); ++p)
      for (ll c = 0; c < ll(k); ++c) {
        if (dp[p][c].val == 0) continue;
        dp[p + 1][c + 0] += dp[p][c] * c;
        dp[p + 1][c + 1] += dp[p][c] * (n - c);
      }
  }
  ModInt ans = 0;
  ModInt invM = 1;
  invM /= m;
  ModInt powInvM = 1;
  for (ll c = 0; c < ll(k + 1); ++c) {
    ans += dp[k][c] * powInvM;
    powInvM *= invM;
  }
  std::cout << (ans);
  std::cout << "\n";
  ;
  return 0;
}

```