#include using namespace std; #define rep(i, n) for(int i = 0; i < n; i++) #define rep2(i, x, n) for(int i = x; i <= n; i++) #define rep3(i, x, n) for(int i = x; i >= n; i--) #define each(e, v) for(auto &e: v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; //const int MOD = 1000000007; const int MOD = 998244353; const int inf = (1<<30)-1; const ll INF = (1LL<<60)-1; template bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;}; template bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;}; struct io_setup{ io_setup(){ ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; template struct Mod_Int{ int x; Mod_Int() : x(0) {} Mod_Int(ll y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Mod_Int &operator += (const Mod_Int &p){ if((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator -= (const Mod_Int &p){ if((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator *= (const Mod_Int &p){ x = (int) (1LL * x * p.x % mod); return *this; } Mod_Int &operator /= (const Mod_Int &p){ *this *= p.inverse(); return *this; } Mod_Int &operator ++ () {return *this += Mod_Int(1);} Mod_Int operator ++ (int){ Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator -- () {return *this -= Mod_Int(1);} Mod_Int operator -- (int){ Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator - () const {return Mod_Int(-x);} Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;} Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;} Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;} Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;} bool operator == (const Mod_Int &p) const {return x == p.x;} bool operator != (const Mod_Int &p) const {return x != p.x;} Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod-2); } Mod_Int pow(ll k) const{ Mod_Int now = *this, ret = 1; for(; k; k >>= 1, now *= now){ if(k&1) ret *= now; } return ret; } friend ostream &operator << (ostream &os, const Mod_Int &p){ return os << p.x; } friend istream &operator >> (istream &is, Mod_Int &p){ ll a; is >> a; p = Mod_Int(a); return is; } }; template struct Combination{ using T = Mod_Int; vector _fac, _ifac; Combination(int n){ _fac.resize(n+1), _ifac.resize(n+1); _fac[0] = 1; rep2(i, 1, n) _fac[i] = _fac[i-1]*i; _ifac[n] = _fac[n].inverse(); rep3(i, n, 1) _ifac[i-1] = _ifac[i]*i; } T fac(int k) const {return _fac[k];} T ifac(int k) const {return _ifac[k];} T comb(int n, int k) const{ if(k < 0 || n < k) return 0; return fac(n)*ifac(n-k)*ifac(k); } T perm(int n, int k) const{ if(k < 0 || n < k) return 0; return fac(n)*ifac(n-k); } T second_stirling_number(int n, int k) const{ T ret = 0; rep(i, k+1){ T tmp = comb(k, i)*T(i).pow(n); ret += ((k-i)&1)? -tmp : tmp; } return ret*ifac(k); } T bell_number(int n, int k) const{ if(n == 0) return 1; chmin(k, n); vector pref(k+1); pref[0] = 1; rep2(i, 1, k){ if(i&1) pref[i] = pref[i-1]-ifac(i); else pref[i] = pref[i-1]+ifac(i); } T ret = 0; rep2(i, 1, k){ ret += T(i).pow(n)*ifac(i)*pref[k-i]; } return ret; } }; using comb = Combination; using mint = Mod_Int<998244353>; template struct Number_Theorem_Transform{ using T = Mod_Int; vector r, ir; Number_Theorem_Transform(){ r.resize(30), ir.resize(30); rep(i, 30){ r[i] = -T(primitive_root).pow((mod-1)>>(i+2)); ir[i] = r[i].inverse(); } } void ntt(vector &a, int n) const{ assert((n&(n-1)) == 0); a.resize(n); for(int k = n; k >>= 1;){ T w = 1; for(int s = 0, t = 0; s < n; s += 2*k){ for(int i = s, j = s+k; i < s+k; i++, j++){ T x = a[i], y = w*a[j]; a[i] = x+y, a[j] = x-y; } w *= r[__builtin_ctz(++t)]; } } } void intt(vector &a, int n) const{ assert((n&(n-1)) == 0); a.resize(n); for(int k = 1; k < n; k <<= 1){ T w = 1; for(int s = 0, t = 0; s < n; s += 2*k){ for(int i = s, j = s+k; i < s+k; i++, j++){ T x = a[i], y = a[j]; a[i] = x+y, a[j] = w*(x-y); } w *= ir[__builtin_ctz(++t)]; } } T inv = T(n).inverse(); for(auto &e: a) e *= inv; } vector convolve(vector a, vector b) const{ int k = sz(a)+sz(b)-1, n = 1; while(n < k) n <<= 1; ntt(a, n), ntt(b, n); rep(i, n) a[i] *= b[i]; intt(a, n), a.resize(k); return a; } }; Number_Theorem_Transform<998244353, 3> NTT; template struct Formal_Power_Series : vector{ using vector :: vector; Formal_Power_Series(const vector &v) : vector(v) {} Formal_Power_Series pre(int n) const{ return Formal_Power_Series(begin(*this), begin(*this)+min((int)this->size(), n)); } Formal_Power_Series rev() const{ Formal_Power_Series ret = *this; reverse(all(ret)); return ret; } Formal_Power_Series &normalize(){ while(!this->empty() && this->back() == 0) this->pop_back(); return *this; } Formal_Power_Series operator - () const noexcept{ Formal_Power_Series ret = *this; rep(i, sz(ret)) ret[i] = -ret[i]; return ret; } Formal_Power_Series &operator += (const T &x){ if(this->empty()) this->resize(1); (*this)[0] += x; return *this; } Formal_Power_Series &operator += (const Formal_Power_Series &v){ if(v.size() > this->size()) this->resize(sz(v)); rep(i, sz(v)) (*this)[i] += v[i]; return this->normalize(); } Formal_Power_Series &operator -= (const T &x){ if(this->empty()) this->resize(1); *this[0] -= x; return *this; } Formal_Power_Series &operator -= (const Formal_Power_Series &v){ if(v.size() > this->size()) this->resize(sz(v)); rep(i, sz(v)) (*this)[i] -= v[i]; return this->normalize(); } Formal_Power_Series &operator *= (const T &x){ rep(i, this->size()) (*this)[i] *= x; return *this; } Formal_Power_Series &operator *= (const Formal_Power_Series &v){ return *this = NTT.convolve(*this, v); } Formal_Power_Series &operator /= (const T &x){ assert(x != 0); T inv = x.inverse(); rep(i, this->size()) (*this)[i] *= inv; return *this; } Formal_Power_Series &operator /= (const Formal_Power_Series &v){ if(v.size() > this->size()){ this->clear(); return *this; } int n = this->size()-sz(v)+1; return *this = (rev().pre(n)*v.rev().inv(n)).pre(n).rev(n); } Formal_Power_Series &operator %= (const Formal_Power_Series &v){ return *this -= (*this/v)*v; } Formal_Power_Series &operator <<= (int x){ Formal_Power_Series ret(x, 0); ret.insert(end(ret), begin(*this), end(*this)); return *this = ret; } Formal_Power_Series &operator >>= (int x){ Formal_Power_Series ret; ret.insert(end(ret), begin(*this)+x, end(*this)); return *this = ret; } Formal_Power_Series operator + (const T &x) const {return Formal_Power_Series(*this) += x;} Formal_Power_Series operator + (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) += v;} Formal_Power_Series operator - (const T &x) const {return Formal_Power_Series(*this) -= x;} Formal_Power_Series operator - (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) -= v;} Formal_Power_Series operator * (const T &x) const {return Formal_Power_Series(*this) *= x;} Formal_Power_Series operator * (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) *= v;} Formal_Power_Series operator / (const T &x) const {return Formal_Power_Series(*this) /= x;} Formal_Power_Series operator / (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) /= v;} Formal_Power_Series operator % (const Formal_Power_Series &v) const {return Formal_Power_Series(*this) %= v;} Formal_Power_Series operator << (int x) const {return Formal_Power_Series(*this) <<= x;} Formal_Power_Series operator >> (int x) const {return Formal_Power_Series(*this) >>= x;} T val(const T &x) const{ T ret = 0; rep3(i, this->size()-1, 0) ret *= x, ret += (*this)[i]; return ret; } Formal_Power_Series diff() const{ // df/dx int n = this->size(); Formal_Power_Series ret(n-1); rep2(i, 1, n-1) ret[i-1] = (*this)[i]*i; return ret; } Formal_Power_Series integral() const{ // ∫fdx int n = this->size(); Formal_Power_Series ret(n+1); rep(i, n) ret[i+1] = (*this)[i]/(i+1); return ret; } Formal_Power_Series inv(int deg) const{ // 1/f (f[0] != 0) assert((*this)[0] != T(0)); Formal_Power_Series ret(1, (*this)[0].inverse()); for(int i = 1; i < deg; i <<= 1){ Formal_Power_Series f = pre(i<<1), g = ret; NTT.ntt(f, 2*i), NTT.ntt(g, 2*i); Formal_Power_Series h(2*i); rep(j, 2*i) h[j] = f[j]*g[j]; NTT.intt(h, 2*i); rep(j, i) h[j] = 0; NTT.ntt(h, 2*i); rep(j, 2*i) h[j] *= g[j]; NTT.intt(h, 2*i); rep(j, i) h[j] = 0; ret -= h; //ret = (ret+ret-ret*ret*pre(i<<1)).pre(i<<1); } ret.resize(deg); return ret; } Formal_Power_Series inv() const {return inv(this->size());} Formal_Power_Series log(int deg) const{ // log(f) (f[0] = 1) assert((*this)[0] == 1); Formal_Power_Series ret = (diff()*inv(deg)).pre(deg-1).integral(); ret.resize(deg); return ret; } Formal_Power_Series log() const {return log(this->size());} Formal_Power_Series exp(int deg) const{ // exp(f) (f[0] = 0) assert((*this)[0] == 0); Formal_Power_Series ret(1, 1); for(int i = 1; i < deg; i <<= 1){ ret = (ret*(pre(i<<1)+1-ret.log(i<<1))).pre(i<<1); } ret.resize(deg); return ret; } Formal_Power_Series exp() const {return exp(this->size());} Formal_Power_Series pow(ll k, int deg) const{ // f^k int n = this->size(); rep(i, n){ if((*this)[i] == 0) continue; T rev = (*this)[i].inverse(); Formal_Power_Series C(*this*rev), D(n-i, 0); rep2(j, i, n-1) D[j-i] = C[j]; D = (D.log()*k).exp()*((*this)[i].pow(k)); Formal_Power_Series E(deg, 0); if(i > 0 && k > deg/i) return E; ll S = i*k; for(int j = 0; j+S < deg && j < D.size(); j++) E[j+S] = D[j]; E.resize(deg); return E; } return Formal_Power_Series(deg, 0); } Formal_Power_Series pow(ll k) const {return pow(k, this->size());} }; using fps = Formal_Power_Series; int main(){ int N, M, K; cin >> N >> M >> K; comb C(N); vector pw(N+1, 1), pw2(N+1, 1); rep(i, N) pw[i+1] = pw[i]*2, pw2[i+1] = pw2[i]*(M-K); fps f(N+1); rep(i, N+1) f[i] = (pw[i]-1)*C.ifac(i); f = f.pow(K); mint ans = 0; rep(i, N+1){ ans += f[i]*pw2[N-i]*C.ifac(N-i); } ans *= C.fac(N)*C.comb(M, K); cout << ans << '\n'; }