#include using namespace std; #define ll long long #define rep(i,n) for(int i=0;i=0;i--) #define rrep2(i,n,k) for(int i=n-1;i>=n-k;i--) #define vll(n,i) vector(n,i) #define v2ll(n,m,i) vector>(n,vll(m,i)) #define v3ll(n,m,k,i) vector>>(n,v2ll(m,k,i)) #define v4ll(n,m,k,l,i) vector>>>(n,v3ll(m,k,l,i)) #define all(v) v.begin(),v.end() #define chmin(k,m) k = min(k,m) #define chmax(k,m) k = max(k,m) #define Pr pair #define Tp tuple #define riano_ std::ios::sync_with_stdio(false);std::cin.tie(nullptr) using Graph = vector>; const ll mod = 998244353; template struct modint{ uint64_t val; constexpr modint(const int64_t val_=0) noexcept:val((val_%int64_t(mod)+int64_t(mod))%int64_t(mod)){} constexpr modint operator-() const noexcept{ return modint(*this)=mod-val; } constexpr modint operator+(const modint rhs) const noexcept{ return modint(*this)+=rhs; } constexpr modint operator-(const modint rhs) const noexcept{ return modint(*this)-=rhs; } constexpr modint operator*(const modint rhs) const noexcept{ return modint(*this)*=rhs; } constexpr modint operator/(const modint rhs) const noexcept{ return modint(*this)/=rhs; } constexpr modint &operator+=(const modint rhs) noexcept{ val+=rhs.val; val-=((val>=mod)?mod:0); return (*this); } constexpr modint &operator-=(const modint rhs) noexcept{ val+=((val>=1; } return (*this)*=now; } modint & operator++(){ val++; if (val == mod) val = 0; return *this; } modint operator++(int){ modint res = *this; ++*this; return res; } constexpr bool operator==(const modint rhs) noexcept{ return val==rhs.val; } constexpr bool operator!=(const modint rhs) noexcept{ return val!=rhs.val; } friend constexpr ostream &operator<<(ostream& os,const modint x) noexcept{ return os<<(x.val); } friend constexpr istream &operator>>(istream& is,modint& x) noexcept{ uint64_t t; is>>t,x=t; return is; } }; typedef modint mint; #define vm(n,i) vector(n,i) #define v2m(n,m,i) vector>(n,vm(m,i)) #define v3m(n,m,k,i) vector>>(n,v2m(m,k,i)) #define v4m(n,m,k,l,i) vector>>>(n,v3m(m,k,l,i)) //累乗 aのb乗、正しmを法として求める long long pw(long long a,long long b,long long m){ if(b==0) return 1; else if(b%2==0){ long long x = pw(a,b/2,m); return (x*x)%m; } else{ long long x = pw(a,b-1,m); return (a*x)%m; } } //行列累乗 matrix power //modをglobalに定義しておく vector> pw_matrix(vector> &M,ll n){ if(n==0){ vector> E = M; rep(i,M.size()){ rep(j,M.size()){ if(i==j) E[i][j] = 1; else E[i][j] = 0; } } return E; } if(n==1) return M; if(n%2==1){ auto K = pw_matrix(M,n-1); int a = M.size(); vector> L(a,vector(a)); rep(i,a){ rep(j,a){ ll b = 0; rep(k,a) b += (M[i][k]*K[k][j])%mod; L[i][j] = b%mod; } } return L; } if(n%2==0){ auto K = pw_matrix(M,n/2); int a = M.size(); vector> L(a,vector(a)); rep(i,a){ rep(j,a){ ll b = 0; rep(k,a) b += (K[i][k]*K[k][j])%mod; L[i][j] = b%mod; } } return L; } } mint sum_r(mint a,mint r, mint n){ if(n==0) return mint(0); mint res = a*mint(pw(r.val,n.val,mod)-1)/(r-mint(1)); return res; } //Combination2 //10^6くらいまで //modはグローバルに定義しておく long long modinv(long long a, long long m) { long long b = m, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= m; if (u < 0) u += m; return u; } vector fact; vector invf; ll comb(ll n,ll k){ if(n<0||k<0||k>n) return 0LL; else{ ll a = fact[n]*invf[k]%mod; a = a*invf[n-k]%mod; return a; } } int main() { riano_; mint ans = 0; ll N,M; cin >> N >> M; //main関数内に以下ペースト //N:max fact.assign(M+N+1,1LL); invf.assign(M+N+1,1LL); rep(i,M+N) fact[i+1] = fact[i]*(i+1)%mod; rep(i,M+N+1) invf[i] = modinv(fact[i],mod); ans = mint(M)*(mint(pw(M,2*N,mod))-mint(pw(M-1,2*N,mod))); mint f[M+1]; for(ll i=2;i<=M;i++){ f[i] = mint(pw(M-i,2*(N-i+1),mod))*mint(comb(N,i-1))*mint(pw(i,i-2,mod))*mint(pw(2,i-1,mod))*mint(fact[i-1]); } for(ll i=2;i<=M;i++){ ans -= f[i]*mint(comb(M,i)); } cout << ans << endl; }