#include <bits/stdc++.h>
using namespace std;
namespace Poly {
const int L = 1 << 20;
const long long P = 998244353LL;
int lim, pos[L];
inline void deb(vector<long long> c) {
  for (int i = 0; i < (int)c.size(); i++)
    printf("%lld%c", c[i], " \n"[i == (int)c.size() - 1]);
}
inline long long fpow(long long x, long long y) {
  long long res = 1;
  for (; y > 0; y >>= 1) {
    if (y & 1) res = res * x % P;
    x = x * x % P;
  }
  return res;
}
const long long inv2 = fpow(2, P - 2);
template <typename T>
inline void inc(T &x, T y) {
  x += y;
  if (x >= P) x -= P;
}
template <typename T>
inline void sub(T &x, T y) {
  x -= y;
  if (x < 0) x += P;
}
inline void prework(int len) {
  int l = 0;
  for (lim = 1; lim < len; lim <<= 1, ++l)
    ;
  for (int i = 0; i < lim; i++)
    pos[i] = (pos[i >> 1] >> 1) | ((i & 1) << (l - 1));
}
inline void ntt(vector<long long> &c, int opt) {
  c.resize(lim, 0);
  for (int i = 0; i < lim; i++)
    if (i < pos[i]) swap(c[i], c[pos[i]]);
  for (int i = 1; i < lim; i <<= 1) {
    long long wn = fpow(3, (P - 1) / (i << 1));
    if (opt == -1) wn = fpow(wn, P - 2);
    for (int len = i << 1, j = 0; j < lim; j += len) {
      long long w = 1;
      for (int k = 0; k < i; k++, w = w * wn % P) {
        long long x = c[j + k], y = w * c[j + k + i] % P;
        c[j + k] = (x + y) % P, c[j + k + i] = (x - y + P) % P;
      }
    }
  }
  if (opt == -1) {
    long long inv = fpow(lim, P - 2);
    for (int i = 0; i < lim; i++) c[i] = c[i] * inv % P;
  }
}
inline vector<long long> operator*(const vector<long long> &x,
                                   const vector<long long> &y) {
  vector<long long> res, u = x, v = y;
  prework(u.size() + v.size() - 1);
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++) res.push_back(v[i] * u[i] % P);
  ntt(res, -1);
  res.resize(u.size() + v.size() - 1);
  return res;
}
vector<long long> mul(const vector<long long> &x, const vector<long long> &y) {
  return x * y;
}
vector<long long> getInv(vector<long long> x, int len) {
  x.resize(len);
  if (len == 1) {
    vector<long long> res;
    res.push_back(fpow(x[0], P - 2));
    return res;
  }
  vector<long long> y = getInv(x, (len + 1) >> 1);
  prework(len << 1);
  vector<long long> u = x, v = y, res;
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++)
    res.push_back(v[i] * (2LL - u[i] * v[i] % P + P) % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
inline void direv(vector<long long> &c) {
  for (int i = 0; i < (int)c.size() - 1; i++) c[i] = c[i + 1] * (i + 1) % P;
  c[c.size() - 1] = 0;
}
inline void integ(vector<long long> &c) {
  for (int i = (int)c.size() - 1; i > 0; i--)
    c[i] = c[i - 1] * fpow(i, P - 2) % P;
  c[0] = 0;
}
inline vector<long long> getLn(vector<long long> c) {
  vector<long long> a = getInv(c, (int)c.size());
  vector<long long> b = c;
  direv(b);
  vector<long long> res = b * a;
  res.resize(c.size());
  integ(res);
  return res;
}
vector<long long> getSqrt(vector<long long> x, int len) {
  x.resize(len);
  if (len == 1) {
    vector<long long> res;
    res.push_back(sqrt(x[0]));
    return res;
  }
  vector<long long> y = getSqrt(x, (len + 1) >> 1);
  vector<long long> u = x, v = y, w, res;
  w = getInv(y, len);
  prework(len << 1);
  ntt(u, 1), ntt(v, 1), ntt(w, 1);
  for (int i = 0; i < lim; i++)
    res.push_back((v[i] * v[i] % P + u[i]) % P * w[i] % P * inv2 % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
vector<long long> getExp(vector<long long> x, int len) {
  x.resize(len, 0);
  if (len == 1) {
    vector<long long> res;
    res.push_back(1);
    return res;
  }
  vector<long long> y = getExp(x, (len + 1) >> 1);
  vector<long long> u = x, v = y, w = y, res;
  w.resize(len, 0);
  w = getLn(w);
  prework(len << 1);
  u[0] = (u[0] + 1 - w[0] + P) % P;
  for (int i = 1; i < (int)u.size(); i++) u[i] = (u[i] - w[i] + P) % P;
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++) res.push_back(u[i] * v[i] % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
inline vector<long long> fpow(vector<long long> x, long long y, int n) {
  x = getLn(x);
  for (int i = 0; i < n; i++) x[i] = x[i] * y % P;
  x = getExp(x, n);
  return x;
}
inline vector<long long> getDiv(vector<long long> x, vector<long long> y) {
  vector<long long> u = x, v = y, res;
  reverse(u.begin(), u.end());
  reverse(v.begin(), v.end());
  int len = x.size() - y.size() + 1;
  u.resize(len, 0), v.resize(len, 0);
  res = getInv(v, len);
  res = mul(u, res);
  res.resize(len);
  reverse(res.begin(), res.end());
  return res;
}
inline vector<long long> getRest(vector<long long> x, vector<long long> y) {
  vector<long long> u = x, v = y, res = getDiv(x, y);
  v = mul(v, res);
  res = u;
  int len = max(u.size(), v.size());
  res.resize(len, 0), v.resize(len, 0);
  for (int i = 0; i < len; i++) res[i] = (res[i] - v[i] + P) % P;
  for (; !res.empty() && !res[res.size() - 1]; res.pop_back())
    ;
  return res;
}
}  // namespace Poly
const int maxn = 5000 + 10;
long long fac[maxn];
int main() {
  const long long mod = Poly::P;
  fac[0] = 1;
  for (int i = 1; i < maxn; ++i) fac[i] = fac[i - 1] * i % mod;
  int n, m, k;
  scanf("%d%d%d", &n, &m, &k);
  long long invm = Poly::fpow(m, mod - 2);
  vector<long long> a(maxn);
  a[1] = 1;
  a = Poly::getExp(a, maxn);
  for (auto &v : a) v = v * invm % mod;
  a[0] = ((a[0] + 1 - invm) % mod + mod) % mod;
  a = Poly::fpow(a, n, maxn);
  cout << a[k] * fac[k] % mod << endl;
  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>
using namespace std;
namespace Poly {
const int L = 1 << 20;
const long long P = 998244353LL;
int lim, pos[L];
inline void deb(vector<long long> c) {
  for (int i = 0; i < (int)c.size(); i++)
    printf("%lld%c", c[i], " \n"[i == (int)c.size() - 1]);
}
inline long long fpow(long long x, long long y) {
  long long res = 1;
  for (; y > 0; y >>= 1) {
    if (y & 1) res = res * x % P;
    x = x * x % P;
  }
  return res;
}
const long long inv2 = fpow(2, P - 2);
template <typename T>
inline void inc(T &x, T y) {
  x += y;
  if (x >= P) x -= P;
}
template <typename T>
inline void sub(T &x, T y) {
  x -= y;
  if (x < 0) x += P;
}
inline void prework(int len) {
  int l = 0;
  for (lim = 1; lim < len; lim <<= 1, ++l)
    ;
  for (int i = 0; i < lim; i++)
    pos[i] = (pos[i >> 1] >> 1) | ((i & 1) << (l - 1));
}
inline void ntt(vector<long long> &c, int opt) {
  c.resize(lim, 0);
  for (int i = 0; i < lim; i++)
    if (i < pos[i]) swap(c[i], c[pos[i]]);
  for (int i = 1; i < lim; i <<= 1) {
    long long wn = fpow(3, (P - 1) / (i << 1));
    if (opt == -1) wn = fpow(wn, P - 2);
    for (int len = i << 1, j = 0; j < lim; j += len) {
      long long w = 1;
      for (int k = 0; k < i; k++, w = w * wn % P) {
        long long x = c[j + k], y = w * c[j + k + i] % P;
        c[j + k] = (x + y) % P, c[j + k + i] = (x - y + P) % P;
      }
    }
  }
  if (opt == -1) {
    long long inv = fpow(lim, P - 2);
    for (int i = 0; i < lim; i++) c[i] = c[i] * inv % P;
  }
}
inline vector<long long> operator*(const vector<long long> &x,
                                   const vector<long long> &y) {
  vector<long long> res, u = x, v = y;
  prework(u.size() + v.size() - 1);
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++) res.push_back(v[i] * u[i] % P);
  ntt(res, -1);
  res.resize(u.size() + v.size() - 1);
  return res;
}
vector<long long> mul(const vector<long long> &x, const vector<long long> &y) {
  return x * y;
}
vector<long long> getInv(vector<long long> x, int len) {
  x.resize(len);
  if (len == 1) {
    vector<long long> res;
    res.push_back(fpow(x[0], P - 2));
    return res;
  }
  vector<long long> y = getInv(x, (len + 1) >> 1);
  prework(len << 1);
  vector<long long> u = x, v = y, res;
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++)
    res.push_back(v[i] * (2LL - u[i] * v[i] % P + P) % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
inline void direv(vector<long long> &c) {
  for (int i = 0; i < (int)c.size() - 1; i++) c[i] = c[i + 1] * (i + 1) % P;
  c[c.size() - 1] = 0;
}
inline void integ(vector<long long> &c) {
  for (int i = (int)c.size() - 1; i > 0; i--)
    c[i] = c[i - 1] * fpow(i, P - 2) % P;
  c[0] = 0;
}
inline vector<long long> getLn(vector<long long> c) {
  vector<long long> a = getInv(c, (int)c.size());
  vector<long long> b = c;
  direv(b);
  vector<long long> res = b * a;
  res.resize(c.size());
  integ(res);
  return res;
}
vector<long long> getSqrt(vector<long long> x, int len) {
  x.resize(len);
  if (len == 1) {
    vector<long long> res;
    res.push_back(sqrt(x[0]));
    return res;
  }
  vector<long long> y = getSqrt(x, (len + 1) >> 1);
  vector<long long> u = x, v = y, w, res;
  w = getInv(y, len);
  prework(len << 1);
  ntt(u, 1), ntt(v, 1), ntt(w, 1);
  for (int i = 0; i < lim; i++)
    res.push_back((v[i] * v[i] % P + u[i]) % P * w[i] % P * inv2 % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
vector<long long> getExp(vector<long long> x, int len) {
  x.resize(len, 0);
  if (len == 1) {
    vector<long long> res;
    res.push_back(1);
    return res;
  }
  vector<long long> y = getExp(x, (len + 1) >> 1);
  vector<long long> u = x, v = y, w = y, res;
  w.resize(len, 0);
  w = getLn(w);
  prework(len << 1);
  u[0] = (u[0] + 1 - w[0] + P) % P;
  for (int i = 1; i < (int)u.size(); i++) u[i] = (u[i] - w[i] + P) % P;
  ntt(u, 1), ntt(v, 1);
  for (int i = 0; i < lim; i++) res.push_back(u[i] * v[i] % P);
  ntt(res, -1);
  res.resize(len);
  return res;
}
inline vector<long long> fpow(vector<long long> x, long long y, int n) {
  x = getLn(x);
  for (int i = 0; i < n; i++) x[i] = x[i] * y % P;
  x = getExp(x, n);
  return x;
}
inline vector<long long> getDiv(vector<long long> x, vector<long long> y) {
  vector<long long> u = x, v = y, res;
  reverse(u.begin(), u.end());
  reverse(v.begin(), v.end());
  int len = x.size() - y.size() + 1;
  u.resize(len, 0), v.resize(len, 0);
  res = getInv(v, len);
  res = mul(u, res);
  res.resize(len);
  reverse(res.begin(), res.end());
  return res;
}
inline vector<long long> getRest(vector<long long> x, vector<long long> y) {
  vector<long long> u = x, v = y, res = getDiv(x, y);
  v = mul(v, res);
  res = u;
  int len = max(u.size(), v.size());
  res.resize(len, 0), v.resize(len, 0);
  for (int i = 0; i < len; i++) res[i] = (res[i] - v[i] + P) % P;
  for (; !res.empty() && !res[res.size() - 1]; res.pop_back())
    ;
  return res;
}
}  // namespace Poly
const int maxn = 5000 + 10;
long long fac[maxn];
int main() {
  const long long mod = Poly::P;
  fac[0] = 1;
  for (int i = 1; i < maxn; ++i) fac[i] = fac[i - 1] * i % mod;
  int n, m, k;
  scanf("%d%d%d", &n, &m, &k);
  long long invm = Poly::fpow(m, mod - 2);
  vector<long long> a(maxn);
  a[1] = 1;
  a = Poly::getExp(a, maxn);
  for (auto &v : a) v = v * invm % mod;
  a[0] = ((a[0] + 1 - invm) % mod + mod) % mod;
  a = Poly::fpow(a, n, maxn);
  cout << a[k] * fac[k] % mod << endl;
  return 0;
}

```