#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(10);
  }
} iosetup;
int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt() : val(0) {}
  ModInt(long long x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(long long exponent) {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &rhs) {
    if ((val += rhs.val) >= mod) val -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &rhs) {
    if ((val += mod - rhs.val) >= mod) val -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &rhs) {
    val = static_cast<unsigned long long>(val) * rhs.val % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &rhs) { return *this *= rhs.inv(); }
  bool operator==(const ModInt &rhs) const { return val == rhs.val; }
  bool operator!=(const ModInt &rhs) const { return val != rhs.val; }
  bool operator<(const ModInt &rhs) const { return val < rhs.val; }
  bool operator<=(const ModInt &rhs) const { return val <= rhs.val; }
  bool operator>(const ModInt &rhs) const { return val > rhs.val; }
  bool operator>=(const ModInt &rhs) const { return val >= rhs.val; }
  ModInt &operator++() {
    if (++val == mod) val = 0;
    return *this;
  }
  ModInt operator++(int) {
    ModInt res = *this;
    ++*this;
    return res;
  }
  ModInt &operator--() {
    val = (val == 0 ? mod : val) - 1;
    return *this;
  }
  ModInt operator--(int) {
    ModInt res = *this;
    --*this;
    return res;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; }
  ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; }
  ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; }
  ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; }
  friend ostream &operator<<(ostream &os, const ModInt &rhs) {
    return os << rhs.val;
  }
  friend istream &operator>>(istream &is, ModInt &rhs) {
    long long x;
    is >> x;
    rhs = ModInt(x);
    return is;
  }

 private:
  ModInt inv() const {
    unsigned a = val, b = mod;
    int x = 1, y = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(x -= tmp * y, y);
    }
    return ModInt(x);
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val;
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000)
      : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    for (int i = (1); i < (val + 1); ++i) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    for (int i = (1); i < (val + 1); ++i) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) {
    if (n < 0 || k < 0) return ModInt(0);
    return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
  }
};
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<ModInt> > dp(k + 1, vector<ModInt>(k + 1, 0));
  dp[0][0] = 1;
  for (int i = (0); i < (k); ++i)
    for (int j = (0); j < (i + 1); ++j) {
      dp[i + 1][j] += dp[i][j] * j;
      dp[i + 1][j + 1] += dp[i][j] * (n - j);
    }
  ModInt ans = 0;
  for (int j = (0); j < (k + 1); ++j) ans += dp[k][j] / ModInt(m).pow(j);
  cout << ans << '\n';
  return 0;
}

### Prompt

Please create a solution in Cpp to 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;
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(10);
  }
} iosetup;
int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt() : val(0) {}
  ModInt(long long x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(long long exponent) {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &rhs) {
    if ((val += rhs.val) >= mod) val -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &rhs) {
    if ((val += mod - rhs.val) >= mod) val -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &rhs) {
    val = static_cast<unsigned long long>(val) * rhs.val % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &rhs) { return *this *= rhs.inv(); }
  bool operator==(const ModInt &rhs) const { return val == rhs.val; }
  bool operator!=(const ModInt &rhs) const { return val != rhs.val; }
  bool operator<(const ModInt &rhs) const { return val < rhs.val; }
  bool operator<=(const ModInt &rhs) const { return val <= rhs.val; }
  bool operator>(const ModInt &rhs) const { return val > rhs.val; }
  bool operator>=(const ModInt &rhs) const { return val >= rhs.val; }
  ModInt &operator++() {
    if (++val == mod) val = 0;
    return *this;
  }
  ModInt operator++(int) {
    ModInt res = *this;
    ++*this;
    return res;
  }
  ModInt &operator--() {
    val = (val == 0 ? mod : val) - 1;
    return *this;
  }
  ModInt operator--(int) {
    ModInt res = *this;
    --*this;
    return res;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &rhs) const { return ModInt(*this) += rhs; }
  ModInt operator-(const ModInt &rhs) const { return ModInt(*this) -= rhs; }
  ModInt operator*(const ModInt &rhs) const { return ModInt(*this) *= rhs; }
  ModInt operator/(const ModInt &rhs) const { return ModInt(*this) /= rhs; }
  friend ostream &operator<<(ostream &os, const ModInt &rhs) {
    return os << rhs.val;
  }
  friend istream &operator>>(istream &is, ModInt &rhs) {
    long long x;
    is >> x;
    rhs = ModInt(x);
    return is;
  }

 private:
  ModInt inv() const {
    unsigned a = val, b = mod;
    int x = 1, y = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(x -= tmp * y, y);
    }
    return ModInt(x);
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val;
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000)
      : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    for (int i = (1); i < (val + 1); ++i) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    for (int i = (1); i < (val + 1); ++i) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) {
    if (n < 0 || k < 0) return ModInt(0);
    return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
  }
};
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<ModInt> > dp(k + 1, vector<ModInt>(k + 1, 0));
  dp[0][0] = 1;
  for (int i = (0); i < (k); ++i)
    for (int j = (0); j < (i + 1); ++j) {
      dp[i + 1][j] += dp[i][j] * j;
      dp[i + 1][j + 1] += dp[i][j] * (n - j);
    }
  ModInt ans = 0;
  for (int j = (0); j < (k + 1); ++j) ans += dp[k][j] / ModInt(m).pow(j);
  cout << ans << '\n';
  return 0;
}

```