#include <bits/stdc++.h>
using namespace std;
const double PI = acos(-1.0);
const long long INF = 1e9 + 47;
const long long LINF = INF * INF;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace IntModulo {
const int mod = 998244353;
inline int add(int x, int y, int m = mod) {
  if (x + y < m) return x + y;
  return x + y - m;
}
inline int sub(int x, int y, int m = mod) {
  if (x >= y) return x - y;
  return x - y + m;
}
inline int mult(int x, int y, int m = mod) { return x * (long long)y % m; }
inline int power(int x, int y, int m = mod) {
  int r = 1;
  while (y) {
    if (y & 1) r = mult(r, x, m);
    x = mult(x, x, m);
    y >>= 1;
  }
  return r;
}
inline int inverse(int x, int m = mod) { return power(x, m - 2, m); }
inline void ADD(int& x, int y, int m = mod) {
  x += y;
  if (x >= m) x -= m;
}
inline void SUB(int& x, int y, int m = mod) {
  x -= y;
  if (x < 0) x += m;
}
inline void MULT(int& x, int y, int m = mod) { x = x * (long long)y % m; }
};  // namespace IntModulo
namespace Combinatorics {
using namespace IntModulo;
const int N = 10000 + 57;
int fact[N];
int inv[N];
int invFact[N];
bool inited = false;
inline int C(int n, int k) {
  return n < k ? 0 : mult(fact[n], mult(invFact[k], invFact[n - k]));
}
inline int H(int n, int k) { return C(n + k - 1, k); }
void init() {
  cerr << "Combinatorics::N"
       << " = " << Combinatorics::N << endl;
  ;
  inited = true;
  inv[1] = 1;
  for (int i = (2); i < (N); ++i) inv[i] = mult(mod - mod / i, inv[mod % i]);
  invFact[0] = fact[0] = 1;
  for (int i = (1); i < (N); ++i) {
    fact[i] = mult(i, fact[i - 1]);
    invFact[i] = mult(invFact[i - 1], inv[i]);
  }
}
};  // namespace Combinatorics
namespace BerlekampMassey {
using namespace IntModulo;
inline vector<int> BM(vector<int> x) {
  vector<int> ls, cur;
  int lf, ld;
  for (int i = (0); i < ((int)((x).size())); ++i) {
    int t = 0;
    for (int j = (0); j < ((int)((cur).size())); ++j)
      t = add(t, mult(x[i - j - 1], cur[j]));
    if (t == x[i]) continue;
    if (!(int)((cur).size())) {
      cur.resize(i + 1);
      lf = i;
      ld = sub(t, x[i]);
      continue;
    }
    int k = mult(sub(t, x[i]), inverse(ld));
    vector<int> c(i - lf - 1);
    c.push_back(k);
    for (int j = (0); j < ((int)((ls).size())); ++j)
      c.push_back(sub(0, mult(k, ls[j])));
    if ((int)((c).size()) < (int)((cur).size())) c.resize((int)((cur).size()));
    for (int j = (0); j < ((int)((cur).size())); ++j) c[j] = add(c[j], cur[j]);
    if (i - lf + (int)((ls).size()) >= (int)((cur).size())) {
      ls = cur;
      lf = i;
      ld = sub(t, x[i]);
    }
    cur = c;
  }
  return cur;
}
inline void multiply(int m, vector<int>& p, vector<int>& q, vector<int>& v) {
  vector<int> t(2 * m, 0);
  for (int i = (0); i < (m); ++i)
    for (int j = (0); j < (m); ++j) t[i + j] = add(t[i + j], mult(p[i], q[j]));
  for (int i = (2 * m) - 1; i >= (m); --i)
    for (int j = (m)-1; j >= (0); --j)
      t[i - j - 1] = add(t[i - j - 1], mult(t[i], v[j]));
  for (int i = (0); i < (m); ++i) p[i] = t[i];
}
inline int solve(vector<int> x, long long n) {
  if ((int)n < (int)((x).size())) return x[n];
  vector<int> v = BM(x);
  int m = v.size();
  if (!m) return 0;
  vector<int> s(m + 1, 0);
  vector<int> t(m + 1, 0);
  s[0] = 1;
  t[1] = 1;
  if (m == 1) t[0] = v[0];
  while (n) {
    if (n & 1) multiply(m, s, t, v);
    multiply(m, t, t, v);
    n >>= 1;
  }
  int ans = 0;
  for (int i = (0); i < (m); ++i) ans = add(ans, mult(s[i], x[i]));
  return ans;
}
};  // namespace BerlekampMassey
namespace LagrangeInterpolation {
using namespace Combinatorics;
int solve(vector<int>& y, long long x) {
  int n = (int)((y).size());
  if ((int)x < n) return y[x];
  if (!Combinatorics::inited) Combinatorics::init();
  vector<int> pref(n);
  pref[0] = 1;
  for (int i = (1); i < (n); ++i) pref[i] = mult(pref[i - 1], (x - i) % mod);
  vector<int> suf(n + 1);
  suf[n] = 1;
  for (int i = (n)-1; i >= (1); --i) suf[i] = mult(suf[i + 1], (x - i) % mod);
  int ans = 0;
  for (int i = (1); i < (n); ++i) {
    int tut = mult(
        y[i], mult(pref[i - 1],
                   mult(suf[i + 1], mult(invFact[i - 1], invFact[n - i - 1]))));
    if ((n - i) & 1)
      ans = add(ans, tut);
    else
      ans = sub(ans, tut);
  }
  return ans;
}
int powerSum(int k, long long n) {
  vector<int> y(k + 3, 0);
  for (int i = (1); i < ((int)((y).size())); ++i)
    y[i] = add(y[i - 1], power(i, k));
  return solve(y, n);
}
};  // namespace LagrangeInterpolation
using namespace IntModulo;
const int N = 10000 + 57;
int p[N];
int q[N];
int x[N];
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  Combinatorics::init();
  p[0] = q[0] = 1;
  p[1] = inverse(m);
  q[1] = sub(1, p[1]);
  for (int i = (2); i < (N); ++i) p[i] = mult(p[i - 1], p[1]);
  for (int i = (2); i < (N); ++i) q[i] = mult(q[i - 1], q[1]);
  for (int i = (1); i < (N); ++i) x[i] = power(i, k);
  vector<int> ans(N, 0);
  for (int nn = (0); nn < (N); ++nn) {
    int tut = 0;
    for (int i = (1); i < (nn + 1); ++i)
      ADD(tut,
          mult(p[i], mult(q[nn - i], mult(x[i], Combinatorics::C(nn, i)))));
    ans[nn] = tut;
  }
  cout << LagrangeInterpolation::solve(ans, n) << endl;
  cerr << "Time elapsed: " << clock() / (double)CLOCKS_PER_SEC << endl;
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 double PI = acos(-1.0);
const long long INF = 1e9 + 47;
const long long LINF = INF * INF;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace IntModulo {
const int mod = 998244353;
inline int add(int x, int y, int m = mod) {
  if (x + y < m) return x + y;
  return x + y - m;
}
inline int sub(int x, int y, int m = mod) {
  if (x >= y) return x - y;
  return x - y + m;
}
inline int mult(int x, int y, int m = mod) { return x * (long long)y % m; }
inline int power(int x, int y, int m = mod) {
  int r = 1;
  while (y) {
    if (y & 1) r = mult(r, x, m);
    x = mult(x, x, m);
    y >>= 1;
  }
  return r;
}
inline int inverse(int x, int m = mod) { return power(x, m - 2, m); }
inline void ADD(int& x, int y, int m = mod) {
  x += y;
  if (x >= m) x -= m;
}
inline void SUB(int& x, int y, int m = mod) {
  x -= y;
  if (x < 0) x += m;
}
inline void MULT(int& x, int y, int m = mod) { x = x * (long long)y % m; }
};  // namespace IntModulo
namespace Combinatorics {
using namespace IntModulo;
const int N = 10000 + 57;
int fact[N];
int inv[N];
int invFact[N];
bool inited = false;
inline int C(int n, int k) {
  return n < k ? 0 : mult(fact[n], mult(invFact[k], invFact[n - k]));
}
inline int H(int n, int k) { return C(n + k - 1, k); }
void init() {
  cerr << "Combinatorics::N"
       << " = " << Combinatorics::N << endl;
  ;
  inited = true;
  inv[1] = 1;
  for (int i = (2); i < (N); ++i) inv[i] = mult(mod - mod / i, inv[mod % i]);
  invFact[0] = fact[0] = 1;
  for (int i = (1); i < (N); ++i) {
    fact[i] = mult(i, fact[i - 1]);
    invFact[i] = mult(invFact[i - 1], inv[i]);
  }
}
};  // namespace Combinatorics
namespace BerlekampMassey {
using namespace IntModulo;
inline vector<int> BM(vector<int> x) {
  vector<int> ls, cur;
  int lf, ld;
  for (int i = (0); i < ((int)((x).size())); ++i) {
    int t = 0;
    for (int j = (0); j < ((int)((cur).size())); ++j)
      t = add(t, mult(x[i - j - 1], cur[j]));
    if (t == x[i]) continue;
    if (!(int)((cur).size())) {
      cur.resize(i + 1);
      lf = i;
      ld = sub(t, x[i]);
      continue;
    }
    int k = mult(sub(t, x[i]), inverse(ld));
    vector<int> c(i - lf - 1);
    c.push_back(k);
    for (int j = (0); j < ((int)((ls).size())); ++j)
      c.push_back(sub(0, mult(k, ls[j])));
    if ((int)((c).size()) < (int)((cur).size())) c.resize((int)((cur).size()));
    for (int j = (0); j < ((int)((cur).size())); ++j) c[j] = add(c[j], cur[j]);
    if (i - lf + (int)((ls).size()) >= (int)((cur).size())) {
      ls = cur;
      lf = i;
      ld = sub(t, x[i]);
    }
    cur = c;
  }
  return cur;
}
inline void multiply(int m, vector<int>& p, vector<int>& q, vector<int>& v) {
  vector<int> t(2 * m, 0);
  for (int i = (0); i < (m); ++i)
    for (int j = (0); j < (m); ++j) t[i + j] = add(t[i + j], mult(p[i], q[j]));
  for (int i = (2 * m) - 1; i >= (m); --i)
    for (int j = (m)-1; j >= (0); --j)
      t[i - j - 1] = add(t[i - j - 1], mult(t[i], v[j]));
  for (int i = (0); i < (m); ++i) p[i] = t[i];
}
inline int solve(vector<int> x, long long n) {
  if ((int)n < (int)((x).size())) return x[n];
  vector<int> v = BM(x);
  int m = v.size();
  if (!m) return 0;
  vector<int> s(m + 1, 0);
  vector<int> t(m + 1, 0);
  s[0] = 1;
  t[1] = 1;
  if (m == 1) t[0] = v[0];
  while (n) {
    if (n & 1) multiply(m, s, t, v);
    multiply(m, t, t, v);
    n >>= 1;
  }
  int ans = 0;
  for (int i = (0); i < (m); ++i) ans = add(ans, mult(s[i], x[i]));
  return ans;
}
};  // namespace BerlekampMassey
namespace LagrangeInterpolation {
using namespace Combinatorics;
int solve(vector<int>& y, long long x) {
  int n = (int)((y).size());
  if ((int)x < n) return y[x];
  if (!Combinatorics::inited) Combinatorics::init();
  vector<int> pref(n);
  pref[0] = 1;
  for (int i = (1); i < (n); ++i) pref[i] = mult(pref[i - 1], (x - i) % mod);
  vector<int> suf(n + 1);
  suf[n] = 1;
  for (int i = (n)-1; i >= (1); --i) suf[i] = mult(suf[i + 1], (x - i) % mod);
  int ans = 0;
  for (int i = (1); i < (n); ++i) {
    int tut = mult(
        y[i], mult(pref[i - 1],
                   mult(suf[i + 1], mult(invFact[i - 1], invFact[n - i - 1]))));
    if ((n - i) & 1)
      ans = add(ans, tut);
    else
      ans = sub(ans, tut);
  }
  return ans;
}
int powerSum(int k, long long n) {
  vector<int> y(k + 3, 0);
  for (int i = (1); i < ((int)((y).size())); ++i)
    y[i] = add(y[i - 1], power(i, k));
  return solve(y, n);
}
};  // namespace LagrangeInterpolation
using namespace IntModulo;
const int N = 10000 + 57;
int p[N];
int q[N];
int x[N];
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  Combinatorics::init();
  p[0] = q[0] = 1;
  p[1] = inverse(m);
  q[1] = sub(1, p[1]);
  for (int i = (2); i < (N); ++i) p[i] = mult(p[i - 1], p[1]);
  for (int i = (2); i < (N); ++i) q[i] = mult(q[i - 1], q[1]);
  for (int i = (1); i < (N); ++i) x[i] = power(i, k);
  vector<int> ans(N, 0);
  for (int nn = (0); nn < (N); ++nn) {
    int tut = 0;
    for (int i = (1); i < (nn + 1); ++i)
      ADD(tut,
          mult(p[i], mult(q[nn - i], mult(x[i], Combinatorics::C(nn, i)))));
    ans[nn] = tut;
  }
  cout << LagrangeInterpolation::solve(ans, n) << endl;
  cerr << "Time elapsed: " << clock() / (double)CLOCKS_PER_SEC << endl;
  return 0;
}

```