#include #include #define rep(i, n) for (int i = 0; i < n; i++) #define ALL(a) a.begin(), a.end() #define ll long long using namespace std; constexpr int mod = 998244353; namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector rts = {{0, 0}, {1, 0}}; vector rev = {0, 1}; void ensure_base(int nbase) { if (nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for (int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while (base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for (int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector &a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for (int i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (int k = 1; k < n; k <<= 1) { for (int i = 0; i < n; i += 2 * k) { for (int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector multiply(const vector &a, const vector &b) { int need = (int)a.size() + (int)b.size() - 1; int nbase = 1; while ((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; vector fa(sz); for (int i = 0; i < sz; i++) { int x = (i < (int)a.size() ? a[i] : 0); int y = (i < (int)b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for (int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for (int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector ret(need); for (int i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } }; template 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); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } 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(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt; template struct ArbitraryModConvolution { using real = FastFourierTransform::real; using C = FastFourierTransform::C; ArbitraryModConvolution() = default; vector multiply(const vector &a, const vector &b, int need = -1) { if (need == -1) need = a.size() + b.size() - 1; int nbase = 0; while ((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); int sz = 1 << nbase; vector fa(sz); for (int i = 0; i < a.size(); i++) { fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15); } fft(fa, sz); vector fb(sz); for (int i = 0; i < b.size(); i++) { fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15); } fft(fb, sz); real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for (int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if (i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector ret(need); for (int i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa).x, bb = T(bb).x, cc = T(cc).x; ret[i] = aa + (bb << 15) + (cc << 30); } return ret; } }; template struct Combination { vector _fact, _rfact, _inv; Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) { _fact[0] = _rfact[sz] = _inv[0] = 1; for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i; _rfact[sz] /= _fact[sz]; for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1); for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1]; } inline T fact(int k) const { return _fact[k]; } inline T rfact(int k) const { return _rfact[k]; } inline T inv(int k) const { return _inv[k]; } T P(int n, int r) const { if (r < 0 || n < r) return 0; return fact(n) * rfact(n - r); } T C(int p, int q) const { if (q < 0 || p < q) return 0; return fact(p) * rfact(q) * rfact(p - q); } T H(int n, int r) const { if (n < 0 || r < 0) return (0); return r == 0 ? 1 : C(n + r - 1, r); } }; template T factorial(int64_t n) { if (n >= mod) return 0; if (n == 0) return 1; const int sn = sqrt(n); const T sn_inv = T(1) / sn; Combination comb(sn); using P = vector; ArbitraryModConvolution fft; auto shift = [&](const P &f, T dx) { int n = (int)f.size(); T a = dx * sn_inv; auto p1 = P(f); for (int i = 0; i < n; i++) { T d = comb.rfact(i) * comb.rfact((n - 1) - i); if (((n - 1 - i) & 1)) d = -d; p1[i] *= d; } auto p2 = P(2 * n); for (int i = 0; i < p2.size(); i++) { p2[i] = (a.x + i - n) <= 0 ? 1 : a + i - n; } for (int i = 1; i < p2.size(); i++) { p2[i] *= p2[i - 1]; } T prod = p2[2 * n - 1]; T prod_inv = T(1) / prod; for (int i = 2 * n - 1; i > 0; --i) { p2[i] = prod_inv * p2[i - 1]; prod_inv *= a + i - n; } p2[0] = prod_inv; auto p3 = fft.multiply(p1, p2, (int)p2.size()); p1 = P(p3.begin() + p1.size(), p3.begin() + p2.size()); prod = 1; for (int i = 0; i < n; i++) { prod *= a + n - 1 - i; } for (int i = n - 1; i >= 0; --i) { p1[i] *= prod; prod *= p2[n + i] * (a + i - n); } return p1; }; function rec = [&](int64_t n) { if (n == 1) return P({1, 1 + sn}); int nh = n >> 1; auto a1 = rec(nh); auto a2 = shift(a1, nh); auto b1 = shift(a1, sn * nh); auto b2 = shift(a1, sn * nh + nh); for (int i = 0; i <= nh; i++) a1[i] *= a2[i]; for (int i = 1; i <= nh; i++) a1.emplace_back(b1[i] * b2[i]); if (n & 1) { for (int64_t i = 0; i < n; i++) { a1[i] *= n + 1LL * sn * i; } T prod = 1; for (int64_t i = 1LL * n * sn; i < 1LL * n * sn + n; i++) { prod *= (i + 1); } a1.push_back(prod); } return a1; }; auto vs = rec(sn); T ret = 1; for (int64_t i = 0; i < sn; i++) ret *= vs[i]; for (int64_t i = 1LL * sn * sn + 1; i <= n; i++) ret *= i; return ret; } modint fac[5050], inv[5050]; void solve() { fac[0] = 1; for (int i = 1; i < 5050; i++) fac[i] = modint(i) * fac[i - 1]; inv[5049] = fac[5049].inverse(); for (int i = 5049; i > 0; i--) inv[i - 1] = modint(i) * inv[i]; int n, m; cin >> n >> m; modint ans = 0; for (int k = 1; k <= n; k++) { modint mul = fac[n] * inv[k] * inv[n - k]; if ((n - k) & 1) mul = -mul; mul *= modint(k).pow(n + m); ans += mul; } ans *= factorial(m); ans /= factorial(n + m) * modint(n).pow(m); cout << ans << '\n'; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(13); solve(); return 0; }