#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define all(a) a.begin(),a.end() #define rep(i, n) for (ll i = 0; i < (n); i++) #define pb push_back #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair P; typedef complex com; constexpr int inf = 1000000010; constexpr ll INF = 1000000000000000010; constexpr ld eps = 1e-12; constexpr ld pi = 3.141592653589793238; template inline bool chmax(T &a, const U &b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T &a, const U &b) { if (a > b) { a = b; return true; } return false; } constexpr ll mod = 998244353; constexpr ll modsize = 200000; vector fac(modsize); vector inv(modsize); vector facinv(modsize); void modcalc() { if (modsize == 0) abort(); fac[0] = 1; fac[1] = 1; inv[1] = 1; facinv[0] = 1; facinv[1] = 1; for (ll i = 2; i < modsize; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod % i] * (mod / i) % mod; facinv[i] = facinv[i - 1] * inv[i] % mod; } } ll modinv(ll a) { if (a == 0) abort(); ll b = mod, u = 1, v = 0; while (b) { ll t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= mod; if (u < 0) u += mod; return u; } ll modpow(ll a, ll b) { ll ans = 1; a %= mod; while (b) { if (b & 1) ans = ans * a % mod; a = a * a % mod; b >>= 1; } return ans; } ll modcomb(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[k] % mod * facinv[n - k] % mod; } ll modperm(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[n - k] % mod; } ll modhom(ll n, ll k) { if (n < 0 || k < 0 || n == 0 && k > 0) return 0; if (n == 0 && k == 0) return 1; return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod; } template class NumberTheoreticTransform { inline static constexpr long long gcd(long long a, long long b) { return (b ? gcd(b, a % b) : a); } inline static long long ext_gcd(long long a, long long b, long long &x, long long &y) { long long res; if (b == 0) res = a, x = 1, y = 0; else res = ext_gcd(b, a%b, y, x), y -= a / b * x; return res; } inline static long long inv_mod(long long a, long long b) { long long x, y; ext_gcd(a, b, x, y); return (x%b + b) % b; } inline static long long pow_mod(long long x, long long n, long long m) { long long res = 1; for (; n > 0; n >>= 1, (x *= x) %= m) if (n & 1) (res *= x) %= m; return res; } inline static long long garner(vector b, vector m, long long d) { int N = b.size(); vector coe(N + 1, 1), val(N + 1, 0); long long g, gl, gr, sum = accumulate(b.begin(), b.end(), 0LL); for (int l = 0; l < N; ++l) { for (int r = l + 1; r < N; ++r) { g = gcd(m[l], m[r]); if (sum && (b[l] - b[r]) % g != 0) return -1; m[l] /= g, m[r] /= g; gl = gcd(m[l], g), gr = g / gl; do { g = gcd(gl, gr); gl *= g, gr /= g; } while (g != 1); m[l] *= gl, m[r] *= gr; b[l] %= m[l], b[r] %= m[r]; } } if (!sum) { long long lcm = 1; for (auto& e : m) (lcm *= e) %= d; return lcm; } m.push_back(d); for (int i = 0; i < N; ++i) { long long t = (b[i] - val[i]) * inv_mod(coe[i], m[i]); ((t %= m[i]) += m[i]) %= m[i]; for (int j = i + 1; j <= N; ++j) { (val[j] += t * coe[j]) %= m[j]; (coe[j] *= m[i]) %= m[j]; } } return val.back(); } inline static void ntt(vector& f, int sgn = 1) { int N = f.size(); int h = pow_mod(root, (mod - 1) / N, mod); if (sgn == -1) h = inv_mod(h, mod); for (int i = 0, j = 1; j < N - 1; ++j) { for (int k = N >> 1; k > (i ^= k); k >>= 1); if (j < i) swap(f[i], f[j]); } for (int i = 1, j = 2; i < N; i *= 2, j *= 2) { long long w = 1, base = pow_mod(h, N / j, mod); for (int k = 0; k < i; ++k, (w *= base) %= mod) { for (int l = k; l < N; l += j) { long long u = f[l]; long long d = f[l + i] * w % mod; f[l] = u + d; if (f[l] >= mod) f[l] -= mod; f[l + i] = u - d; if (f[l + i] < 0) f[l + i] += mod; } } } for (auto& x : f) if (x < 0) x += mod; } public: inline static vector convolution(vector g, vector h) { int N; for (N = 1; N < g.size() + h.size(); N *= 2); vector f(N); g.resize(N); h.resize(N); ntt(g); ntt(h); for (int i = 0; i < N; ++i) (f[i] = g[i] * h[i]) %= mod; ntt(f, -1); long long inv = inv_mod(N, mod); for (auto& x : f) x = x * inv % mod; return f; } inline static vector convolution_arbitrarymod(vector g, vector h) { for (auto& a : g) a %= mod; for (auto& a : h) a %= mod; const int mod1 = 167772161; const int mod2 = 469762049; const int mod3 = 1224736769; auto x = NumberTheoreticTransform::convolution(g, h); auto y = NumberTheoreticTransform::convolution(g, h); auto z = NumberTheoreticTransform::convolution(g, h); vector res(x.size()), b(3), m(3); for (int i = 0; i < x.size(); ++i) { m[0] = mod1, b[0] = x[i]; m[1] = mod2, b[1] = y[i]; m[2] = mod3, b[2] = z[i]; res[i] = garner(b, m, mod); } return res; } }; signed main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); modcalc(); ll n, k; cin >> n >> k; vector a(k + 1), b(k + 1); rep(i, k + 1) { if (i & 1) b[i] = facinv[i]; if ((k & 1) != (i & 1)) a[i] = modpow(i, n) * facinv[i] % mod; else { a[i] = mod - modpow(i, n) * facinv[i] % mod; if (a[i] >= mod) a[i] -= mod; } } vector c = NumberTheoreticTransform<998244353>::convolution(a, b); ll ans = 0; rep(i, k + 1) ans += c[i] * facinv[k - i] % mod; ans %= mod; cout << ans * fac[k] % mod << '\n'; }