結果

問題 No.1321 塗るめた
ユーザー 👑 tute7627tute7627
提出日時 2020-12-18 18:29:08
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 331 ms / 2,000 ms
コード長 18,762 bytes
コンパイル時間 3,705 ms
コンパイル使用メモリ 243,160 KB
実行使用メモリ 9,976 KB
最終ジャッジ日時 2024-09-21 09:14:05
合計ジャッジ時間 13,211 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 8 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 3 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 156 ms
7,256 KB
testcase_13 AC 322 ms
9,012 KB
testcase_14 AC 148 ms
6,272 KB
testcase_15 AC 152 ms
6,396 KB
testcase_16 AC 158 ms
7,300 KB
testcase_17 AC 8 ms
5,376 KB
testcase_18 AC 326 ms
9,524 KB
testcase_19 AC 74 ms
5,376 KB
testcase_20 AC 150 ms
6,280 KB
testcase_21 AC 324 ms
9,580 KB
testcase_22 AC 328 ms
9,972 KB
testcase_23 AC 329 ms
9,972 KB
testcase_24 AC 327 ms
9,848 KB
testcase_25 AC 328 ms
9,972 KB
testcase_26 AC 331 ms
9,936 KB
testcase_27 AC 330 ms
9,972 KB
testcase_28 AC 329 ms
9,972 KB
testcase_29 AC 327 ms
9,972 KB
testcase_30 AC 326 ms
9,844 KB
testcase_31 AC 327 ms
9,972 KB
testcase_32 AC 157 ms
7,256 KB
testcase_33 AC 149 ms
6,136 KB
testcase_34 AC 156 ms
7,120 KB
testcase_35 AC 149 ms
6,144 KB
testcase_36 AC 326 ms
9,968 KB
testcase_37 AC 327 ms
9,976 KB
testcase_38 AC 327 ms
9,968 KB
testcase_39 AC 325 ms
9,848 KB
testcase_40 AC 328 ms
9,976 KB
testcase_41 AC 328 ms
9,840 KB
testcase_42 AC 2 ms
5,376 KB
testcase_43 AC 156 ms
7,380 KB
testcase_44 AC 149 ms
6,140 KB
testcase_45 AC 157 ms
7,124 KB
testcase_46 AC 34 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<ll>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<ll>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
  }
  friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
  }
  friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
  }
  friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
  }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
using modint = ModInt< MOD9 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);}
//using modint=ld;
template< typename T >
struct FormalPowerSeries : vector< T > {
  using vector< T >::vector;
  using P = FormalPowerSeries;

  using MULT = function< P(P, P) >;
  using FFT = function< void(P &) >;
  using SQRT = function< T(T) >;

  static MULT &get_mult() {
    static MULT mult = nullptr;
    return mult;
  }

  static void set_mult(MULT f) {
    get_mult() = f;
  }

  static FFT &get_fft() {
    static FFT fft = nullptr;
    return fft;
  }

  static FFT &get_ifft() {
    static FFT ifft = nullptr;
    return ifft;
  }

  static void set_fft(FFT f, FFT g) {
    get_fft() = f;
    get_ifft() = g;
  }

  static SQRT &get_sqrt() {
    static SQRT sqr = nullptr;
    return sqr;
  }

  static void set_sqrt(SQRT sqr) {
    get_sqrt() = sqr;
  }

  void shrink() {
    while(this->size() && this->back() == T(0)) this->pop_back();
  }

  P operator+(const P &r) const { return P(*this) += r; }

  P operator+(const T &v) const { return P(*this) += v; }

  P operator-(const P &r) const { return P(*this) -= r; }

  P operator-(const T &v) const { return P(*this) -= v; }

  P operator*(const P &r) const { return P(*this) *= r; }

  P operator*(const T &v) const { return P(*this) *= v; }

  P operator/(const P &r) const { return P(*this) /= r; }

  P operator%(const P &r) const { return P(*this) %= r; }

  P &operator+=(const P &r) {
    if(r.size() > this->size()) this->resize(r.size());
    for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
    return *this;
  }

  P &operator+=(const T &r) {
    if(this->empty()) this->resize(1);
    (*this)[0] += r;
    return *this;
  }

  P &operator-=(const P &r) {
    if(r.size() > this->size()) this->resize(r.size());
    for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
    //shrink();
    return *this;
  }

  P &operator-=(const T &r) {
    if(this->empty()) this->resize(1);
    (*this)[0] -= r;
    //shrink();
    return *this;
  }

  P &operator*=(const T &v) {
    const int n = (int) this->size();
    for(int k = 0; k < n; k++) (*this)[k] *= v;
    return *this;
  }

  P &operator*=(const P &r) {
    if(this->empty() || r.empty()) {
      this->clear();
      return *this;
    }
	 if(min(this->size(), r.size()) < 5 || get_mult() == nullptr){
      P ret(this->size() + r.size() - 1);
      for(int i = 0; i < this->size(); i++){
        for(int j = 0; j < r.size(); j++){
          ret[i + j] += (*this)[i] * r[j];
        }
      }
      return *this = ret;
    }
    return *this = get_mult()(*this, r);
  }

  P &operator%=(const P &r) { return *this -= *this / r * r; }

  P operator-() const {
    P ret(this->size());
    for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
    return ret;
  }

  P &operator/=(const P &r) {
    if(this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
  }

  P dot(P r) const {
    P ret(min(this->size(), r.size()));
    for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
    return ret;
  }

  P pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); }

  P operator>>(int sz) const {
    if(this->size() <= sz) return {};
    P ret(*this);
    ret.erase(ret.begin(), ret.begin() + sz);
    return ret;
  }

  P operator<<(int sz) const {
    P ret(*this);
    ret.insert(ret.begin(), sz, T(0));
    return ret;
  }

  P rev(int deg = -1) const {
    P ret(*this);
    if(deg != -1) ret.resize(deg, T(0));
    reverse(begin(ret), end(ret));
    return ret;
  }

  P diff() const {
    const int n = (int) this->size();
    P ret(max(0, n - 1));
    for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
    return ret;
  }

  P integral() const {
    const int n = (int) this->size();
    P ret(n + 1);
    ret[0] = T(0);
    for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
    return ret;
  }

  // F(0) must not be 0
  P inv(int deg = -1) const {
    assert(((*this)[0]) != T(0));
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    if(get_fft() != nullptr) {
      P ret(*this);
      ret.resize(deg, T(0));
      return ret.inv_fast();
    }
    P ret({T(1) / (*this)[0]});
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
    }
    return ret.pre(deg);
  }

  // F(0) must be 1
  P log(int deg = -1) const {
    assert((*this)[0] == 1);
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  P sqrt(int deg = -1) const {
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    if((*this)[0] == T(0)) {
      for(int i = 1; i < n; i++) {
        if((*this)[i] != T(0)) {
          if(i & 1) return {};
          if(deg - i / 2 <= 0) break;
          auto ret = (*this >> i).sqrt(deg - i / 2);
          if(ret.empty()) return {};
          ret = ret << (i / 2);
          if(ret.size() < deg) ret.resize(deg, T(0));
          return ret;
        }
      }
      return P(deg, 0);
    }

    P ret;
    if(get_sqrt() == nullptr) {
      assert((*this)[0] == T(1));
      ret = {T(1)};
    } else {
      auto sqr = get_sqrt()((*this)[0]);
      if(sqr * sqr != (*this)[0]) return {};
      ret = {T(sqr)};
    }

    T inv2 = T(1) / T(2);
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
    }
    return ret.pre(deg);
  }

  // F(0) must be 0
  P exp(int deg = -1) const {
    assert((*this)[0] == T(0));
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    if(get_fft() != nullptr) {
      P ret(*this);
      ret.resize(deg, T(0));
      return ret.exp_rec();
    }
    P ret({T(1)});
    for(int i = 1; i < deg; i <<= 1) {
      ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
    }
    return ret.pre(deg);
  }


  P online_convolution_exp(const P &conv_coeff) const {
    const int n = (int) conv_coeff.size();
    assert((n & (n - 1)) == 0);
    vector< P > conv_ntt_coeff;
    auto& fft = get_fft();
    auto& ifft = get_ifft();
    for(int i = n; i >= 1; i >>= 1) {
      P g(conv_coeff.pre(i));
      fft(g);
      conv_ntt_coeff.emplace_back(g);
    }
    P conv_arg(n), conv_ret(n);
    auto rec = [&](auto rec, int l, int r, int d) -> void {
      if(r - l <= 16) {
        for(int i = l; i < r; i++) {
          T sum = 0;
          for(int j = l; j < i; j++) sum += conv_arg[j] * conv_coeff[i - j];
          conv_ret[i] += sum;
          conv_arg[i] = i == 0 ? T(1) : conv_ret[i] / i;
        }
      } else {
        int m = (l + r) / 2;
        rec(rec, l, m, d + 1);
        P pre(r - l);
        for(int i = 0; i < m - l; i++) pre[i] = conv_arg[l + i];
        fft(pre);
        for(int i = 0; i < r - l; i++) pre[i] *= conv_ntt_coeff[d][i];
        ifft(pre);
        for(int i = 0; i < r - m; i++) conv_ret[m + i] += pre[m + i - l];
        rec(rec, m, r, d + 1);
      }
    };
    rec(rec, 0, n, 0);
    return conv_arg;
  }

  P exp_rec() const {
    assert((*this)[0] == T(0));
    const int n = (int) this->size();
    int m = 1;
    while(m < n) m *= 2;
    P conv_coeff(m);
    for(int i = 1; i < n; i++) conv_coeff[i] = (*this)[i] * i;
    return online_convolution_exp(conv_coeff).pre(n);
  }


  P inv_fast() const {
    assert(((*this)[0]) != T(0));

    const int n = (int) this->size();
    P res{T(1) / (*this)[0]};

    for(int d = 1; d < n; d <<= 1) {
      P f(2 * d), g(2 * d);
      for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];
      for(int j = 0; j < d; j++) g[j] = res[j];
      get_fft()(f);
      get_fft()(g);
      for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
      get_ifft()(f);
      for(int j = 0; j < d; j++) {
        f[j] = 0;
        f[j + d] = -f[j + d];
      }
      get_fft()(f);
      for(int j = 0; j < 2 * d; j++) f[j] *= g[j];
      get_ifft()(f);
      for(int j = 0; j < d; j++) f[j] = res[j];
      res = f;
    }
    return res.pre(n);
  }

  P pow(int64_t k, int deg = -1) const {
    const int n = (int) this->size();
    if(deg == -1) deg = n;
    for(int i = 0; i < n; i++) {
      if((*this)[i] != T(0)) {
        T rev = T(1) / (*this)[i];
        P ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
        if(i * k > deg) return P(deg, T(0));
        ret = (ret << (i * k)).pre(deg);
        if(ret.size() < deg) ret.resize(deg, T(0));
        return ret;
      }
    }
    return *this;
  }

  T eval(T x) const {
    T r = 0, w = 1;
    for(auto &v : *this) {
      r += w * v;
      w *= x;
    }
    return r;
  }

  P pow_mod(int64_t n, P mod) const {
    P modinv = mod.rev().inv();
    auto get_div = [&](P base) {
      if(base.size() < mod.size()) {
        base.clear();
        return base;
      }
      int n = base.size() - mod.size() + 1;
      return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
    };
    P x(*this), ret{1};
    while(n > 0) {
      if(n & 1) {
        ret *= x;
        ret -= get_div(ret) * mod;
      }
      x *= x;
      x -= get_div(x) * mod;
      n >>= 1;
    }
    return ret;
  }
    void mul(vector<pair<int, T>> g, bool extend = false){
    if(extend)this->resize(this->size() + g.back().first);
    int n = this->size();
    int d = g[0].first;
    T c = g[0].second;
    if(d == 0)g.erase(g.begin());
    else c = 0;
    for(int i = n - 1; i >= 0; i--){
      (*this)[i] *= c;
      for(auto z : g){
        if(z.first > i)continue;
        (*this)[i] += (*this)[i-z.first] * z.second;
      }
    }
  }
  void div(vector<pair<int, T>>g){//定数項は非ゼロ
    int n = this->size();
    int d = g[0].first;
    T c = g[0].second;
    c = T(1) / c;
    g.erase(g.begin());
    for(int i = 0; i < n; i++){
      for(auto z : g){
        if(z.first > i)continue;
        (*this)[i] -= (*this)[i-z.first] * z.second;
      }
      (*this)[i] *= c;
    }
  }
};

template< typename T >
FormalPowerSeries< T > stirling_second_kth_column(int N, int K) {
  FormalPowerSeries< T > poly(N + 1), ret(N + 1);
  poly[1] = 1;
  poly = poly.exp();
  poly[0] -= 1;
  poly = poly.pow(K);
  T rev = 1, mul = 1;
  for(int i = 2; i <= K; i++) rev *= i;
  rev = T(1) / rev;
  poly *= rev;
  for(int i = 0; i <= N; i++) {
    ret[i] = poly[i] * mul;
    mul *= i + 1;
  }
  return ret;
}
template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {

  vector< Mint > dw, idw;
  int max_base;
  Mint root;

  NumberTheoreticTransformFriendlyModInt() {
    const unsigned mod = Mint::get_mod();
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while(tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while(root.pow((mod - 1) >> 1) == 1) root += 1;
    assert(root.pow(mod - 1) == 1);
    dw.resize(max_base);
    idw.resize(max_base);
    for(int i = 0; i < max_base; i++) {
      dw[i] = -root.pow((mod - 1) >> (i + 2));
      idw[i] = Mint(1) / dw[i];
    }
  }

  void ntt(vector< Mint > &a) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    assert(__builtin_ctz(n) <= max_base);
    for(int m = n; m >>= 1;) {
      Mint w = 1;
      for(int s = 0, k = 0; s < n; s += 2 * m) {
        for(int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j] * w;
          a[i] = x + y, a[j] = x - y;
        }
        w *= dw[__builtin_ctz(++k)];
      }
    }
  }

  void intt(vector< Mint > &a, bool f = true) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    assert(__builtin_ctz(n) <= max_base);
    for(int m = 1; m < n; m *= 2) {
      Mint w = 1;
      for(int s = 0, k = 0; s < n; s += 2 * m) {
        for(int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * w;
        }
        w *= idw[__builtin_ctz(++k)];
      }
    }
    if(f) {
      Mint inv_sz = Mint(1) / n;
      for(int i = 0; i < n; i++) a[i] *= inv_sz;
    }
  }

  vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {
    int need = a.size() + b.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    int sz = 1 << nbase;
    a.resize(sz, 0);
    b.resize(sz, 0);
    ntt(a);
    ntt(b);
    Mint inv_sz = Mint(1) / sz;
    for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
    intt(a, false);
    a.resize(need);
    return a;
  }
};
template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;

  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(ll k) const { return _fact[k]; }

  inline T rfact(ll k) const { return _rfact[k]; }

  inline T inv(ll k) const { return _inv[k]; }

  T P(ll n, ll r) const {
    if(r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }

  T C(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  
  T RC(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }

  T H(ll n, ll r) const {
    if(n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
using Comb=Combination<modint>;
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  using FPS=FormalPowerSeries<modint>;
  NumberTheoreticTransformFriendlyModInt<modint> ntt;
  auto mult=[&](const FPS &x,const FPS &y){
    auto ret = ntt.multiply(x,y);
    return FPS(ret.begin(),ret.end());
  };
  FPS::set_mult(mult);
  FPS::set_fft([&](FPS &a){return ntt.ntt(a);},[&](FPS &b){return ntt.intt(b);});
  ll n,m,k;cin>>n>>m>>k;
  FPS str=stirling_second_kth_column<modint>(n+1,k);
  Comb comb(n+2);
  modint ret=0;
  rep(i,1,n+1){
    //cout<<comb.C(m,k) spa comb.C(n,i) spa str[i] spa pow(m,n-i)<<endl;
    ret+=comb.C(m,k)*comb.C(n,i)*str[i]*pow(m,n-i)*comb.fact(k);
  }
  cout<<ret<<endl;
  return 0;
}
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