#include namespace { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic pop using namespace std; using namespace atcoder; #define rep(i,n)for (int i = 0; i < int(n); ++i) #define rrep(i,n)for (int i = int(n)-1; i >= 0; --i) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template void chmax(T& a, const T& b) { a = max(a, b); } template void chmin(T& a, const T& b) { a = min(a, b); } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; constexpr int FACT_SIZE = 1000000; mint Fact[FACT_SIZE + 1]; mint iFact[FACT_SIZE + 1]; const auto fact_init = [] { Fact[0] = mint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }(); mint comb(int n, int k) { if (k == 0) return mint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return mint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } mint icomb(int n, int k) { return iFact[n] * Fact[n - k] * Fact[k]; } mint fact(int n) {return Fact[n];} mint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m; cin >> n >> m; // vector e(m + 1); // rep(i, m + 1) { // if (i % 2 == 0) e[i] = iFact[i]; // else e[i] = -iFact[i]; // } // vector f(m + 1); // rep(i, m + 1) { // f[i] = mint(i).pow(2 * n) * iFact[i]; // } // f = convolution(f, e); // f.resize(m + 1); mint ans = m * mint(m).pow(2 * n); // rep(i, m + 1) ans += i * f[i] * Fact[i]; // remove for tree case for(int i = 1; i <= m; i++) { if (i - 1 > n) break; mint tmp = i == 1 ? mint(1) : mint(i).pow(i - 2) * Fact[i - 1] * mint(2).pow(i - 1); ans -= comb(m, i) * comb(n, i - 1) * mint(m - i).pow(2 * (n - (i - 1))) * tmp; } cout << ans.val() << '\n'; }