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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1.1e6 + 5;
const int inv2 = 499122177;
int wn[MAXN], wnn[MAXN], fac[MAXN], facn[MAXN], f[MAXN], g[MAXN];
int n, m, k, Inv[MAXN], rev[MAXN], a[MAXN], b[MAXN], e[MAXN], d[MAXN], c[MAXN],
    A[MAXN], B[MAXN], D[MAXN], G[MAXN], AA[MAXN], BB[MAXN], AAA[MAXN],
    BBB[MAXN], X[MAXN];
const int mod = 998244353;
long long Sc() {
  long long ret = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  for (; isdigit(ch); ch = getchar())
    ret = ret * 10 + ch - 48, ret = ret >= mod ? ret % mod : ret;
  return ret * f;
}
char buf[121], *p1 = buf, *p2 = buf;
inline int getc() {
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 121, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int read() {
  int ret = 0, f = 0;
  char ch = getc();
  while (!isdigit(ch)) {
    if (ch == '-') f = 1;
    ch = getc();
  }
  while (isdigit(ch)) {
    ret = ret * 10 + ch - 48;
    ch = getc();
  }
  return f ? -ret : ret;
}
template <typename T>
inline void write(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
int mul(int a, int b) { return 1ll * a * b % mod; }
int dec(int a, int b) { return a >= b ? a - b : a + mod - b; }
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
long long qkpow(long long a, long long b, long long mod) {
  long long ans = 1, base = a;
  while (b) {
    if (b & 1) ans = mul(ans, base);
    base = mul(base, base);
    b >>= 1;
  }
  return ans;
}
void init() {
  Inv[1] = 1;
  for (int i = 2; i < MAXN; i++)
    Inv[i] = 1ll * (mod - mod / i) * Inv[mod % i] % mod;
  for (int i = 1; i < MAXN; i <<= 1)
    wn[i] = qkpow(3ll, (mod - 1) / (i << 1), mod),
    wnn[i] = qkpow(wn[i], mod - 2, mod);
}
void NTT(int *a, int type, int n) {
  for (int i = 0; i < n; i++)
    if (i < rev[i]) swap(a[i], a[rev[i]]);
  for (int mid = 1; mid < n; mid <<= 1) {
    int Wn = wn[mid];
    if (type == -1) Wn = wnn[mid];
    for (int R = mid << 1, j = 0; j < n; j += R) {
      int w = 1;
      for (int k = 0; k < mid; k++, w = mul(w, Wn)) {
        int x = a[j + k], y = mul(w, a[j + mid + k]);
        a[j + k] = add(x, y);
        a[j + mid + k] = dec(x, y);
      }
    }
  }
  if (type == -1)
    for (int i = 0; i < n; i++) a[i] = mul(a[i], Inv[n]);
}
void Polyinv(int *a, int *b, int len) {
  if (len == 1) {
    b[0] = qkpow(a[0], mod - 2, mod);
    return;
  }
  Polyinv(a, b, (len + 1) >> 1);
  int l = 0, m = (len << 1), n = 1;
  for (; n <= m; n <<= 1, l++)
    ;
  for (int i = 0; i < n; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  for (int i = 0; i < len; i++) c[i] = a[i];
  for (int i = len; i < n; i++) c[i] = 0;
  NTT(c, 1, n), NTT(b, 1, n);
  for (int i = 0; i < n; i++) b[i] = mul(dec(2, mul(c[i], b[i])), b[i]);
  NTT(b, -1, n);
  for (int i = len; i < n; i++) b[i] = 0;
}
void Polydao(int *Aa, int *Bb, int len) {
  Bb[len - 1] = 0;
  for (int i = 1; i < len; i++) Bb[i - 1] = mul(i, Aa[i]);
}
void Polyjifen(int *Aa, int *Bb, int len) {
  Bb[0] = 0;
  for (int i = 1; i < len; i++) Bb[i] = mul(Inv[i], Aa[i - 1]);
}
void PolyIn(int *f, int *g, int n) {
  static int A[MAXN], B[MAXN];
  int l = 0, M = 2 * n, N = 1;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++) A[i] = B[i] = 0;
  Polydao(f, A, n);
  Polyinv(f, B, n);
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(A, 1, N), NTT(B, 1, N);
  for (int i = 0; i < N; i++) A[i] = mul(A[i], B[i]);
  NTT(A, -1, N);
  Polyjifen(A, g, n);
}
void PolyExp(int *f, int *g, int n) {
  if (n == 1) {
    g[0] = 1;
    return;
  }
  PolyExp(f, g, (n + 1) >> 1);
  PolyIn(g, d, n);
  int M = (n << 1), N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  for (int i = 0; i < n; i++) d[i] = dec(f[i], d[i]);
  for (int i = n; i < N; i++) d[i] = g[i] = 0;
  d[0]++;
  NTT(d, 1, N), NTT(g, 1, N);
  for (int i = 0; i < N; i++) g[i] = mul(g[i], d[i]);
  NTT(g, -1, N);
  for (int i = n; i < N; i++) g[i] = 0;
}
void Polyqkpow(int *F, int *G, int k, int n) {
  for (int i = 0; i < n; i++) D[i] = G[i] = 0;
  PolyIn(F, D, n);
  for (int i = 0; i < n; i++) D[i] = mul(D[i], k);
  PolyExp(D, G, n);
}
void Polysqrt(int *f, int *g, int n) {
  if (n == 1) {
    g[0] = qkpow(f[0], mod - 2, mod);
    return;
  }
  Polysqrt(f, g, (n + 1) >> 1);
  int M = 2 * n, N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  for (int i = 0; i < n; i++) A[i] = f[i], B[i] = 0;
  for (int i = n; i < N; i++) A[i] = 0, B[i] = 0;
  Polyinv(g, B, n);
  NTT(A, 1, N), NTT(B, 1, N);
  for (int i = 0; i < N; i++) A[i] = mul(A[i], B[i]);
  NTT(A, -1, N);
  for (int i = 0; i < n; i++) g[i] = mul(add(g[i], A[i]), inv2);
}
void Polysin(int *f, int *g, int n) {
  int ecsy = 86583718, fuecsy = 911660635, iinv = qkpow(ecsy, mod - 2, mod);
  for (int i = 0; i < n; i++) A[i] = mul(f[i], ecsy), B[i] = mul(f[i], fuecsy);
  PolyExp(A, AAA, n), PolyExp(B, BBB, n);
  for (int i = 0; i < n; i++) g[i] = mul(mul(dec(AAA[i], BBB[i]), inv2), iinv);
}
void Polycos(int *f, int *g, int n) {
  int ecsy = 86583718, fuecsy = 911660635;
  for (int i = 0; i < n; i++) A[i] = mul(f[i], ecsy), B[i] = mul(f[i], fuecsy);
  PolyExp(A, AAA, n), PolyExp(B, BBB, n);
  for (int i = 0; i < n; i++) g[i] = mul(add(AAA[i], BBB[i]), inv2);
}
void Polyasin(int *f, int *g, int n) {
  static int fbie[MAXN], FF[MAXN], A[MAXN], B[MAXN], Fs[MAXN], Finv[MAXN];
  for (int i = 0; i < (n << 1); i++)
    fbie[i] = FF[i] = A[i] = B[i] = Fs[i] = Finv[i] = 0;
  Polydao(f, fbie, n);
  int M = (n << 1), N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < n; i++) A[i] = B[i] = f[i];
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(A, 1, N), NTT(B, 1, N);
  for (int i = 0; i < N; i++) FF[i] = mul(A[i], B[i]);
  NTT(FF, -1, N);
  for (int i = 0; i < n; i++) FF[i] = dec(i == 0 ? 1 : 0, FF[i]);
  for (int i = n; i < N; i++) FF[i] = 0;
  Polysqrt(FF, Fs, n);
  Polyinv(Fs, Finv, n);
  M = (n << 1), N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(fbie, 1, N), NTT(Finv, 1, N);
  for (int i = 0; i < N; i++) fbie[i] = mul(fbie[i], Finv[i]);
  NTT(fbie, -1, N);
  Polyjifen(fbie, g, n);
}
void Polyatan(int *f, int *g, int n) {
  static int fbie[MAXN], FF[MAXN], A[MAXN], B[MAXN], Finv[MAXN];
  for (int i = 0; i < (n << 1); i++)
    fbie[i] = FF[i] = A[i] = B[i] = Finv[i] = 0;
  Polydao(f, fbie, n);
  int M = (n << 1), N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < n; i++) A[i] = B[i] = f[i];
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(A, 1, N), NTT(B, 1, N);
  for (int i = 0; i < N; i++) FF[i] = mul(A[i], B[i]);
  NTT(FF, -1, N);
  for (int i = 0; i < n; i++) FF[i] = add(i == 0 ? 1 : 0, FF[i]);
  for (int i = n; i < N; i++) FF[i] = 0;
  Polyinv(FF, Finv, n);
  M = (n << 1), N = 1, l = 0;
  for (; N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(fbie, 1, N), NTT(Finv, 1, N);
  for (int i = 0; i < N; i++) fbie[i] = mul(fbie[i], Finv[i]);
  NTT(fbie, -1, N);
  Polyjifen(fbie, g, n);
}
void mul(int *s, int *a, int len) {
  static int t[MAXN];
  __builtin_memcpy(t, a, sizeof(int) * len);
  NTT(s, 1, len), NTT(t, 1, len);
  for (int i = 0; i < len; i++) s[i] = mul(s[i], t[i]);
  NTT(s, -1, len);
  for (int i = 0; i < len; i++) s[i] = !!s[i];
}
int main() {
  init();
  scanf("%d %d %d", &n, &m, &k);
  fac[0] = facn[0] = 1;
  for (int i = 1; i < k + 1; i++)
    fac[i] = mul(fac[i - 1], i), facn[i] = qkpow(fac[i], mod - 2, mod);
  for (int i = 0; i < k + 1; i++)
    f[i] = mul(qkpow(mod - 1, i, mod), facn[i]),
    g[i] = mul(qkpow(i, k, mod), facn[i]);
  int l = 0, M, N = 1;
  for (M = 2 * (k + 1); N <= M; N <<= 1, l++)
    ;
  for (int i = 0; i < N; i++)
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (l - 1));
  NTT(f, 1, N), NTT(g, 1, N);
  for (int i = 0; i < N; i++) f[i] = mul(f[i], g[i]);
  NTT(f, -1, N);
  long long now = 1, ans = 0;
  for (int j = 0; j <= min(k, n); j++) {
    ans = add(ans, mul(mul(mul(f[j], fac[j]), now), qkpow(m, n - j, mod)));
    now = mul(now, n - j), now = mul(now, qkpow(j + 1, mod - 2, mod));
  }
  printf("%d", mul(ans, qkpow(qkpow(m, n, mod), mod - 2, mod)));
  return 0;
}