#pragma region Macros #pragma GCC optimize("O3") #include #define ll long long #define ld long double #define rep2(i, a, b) for(ll i = a; i <= b; ++i) #define rep(i, n) for(ll i = 0; i < n; ++i) #define rep3(i, a, b) for(ll i = a; i >= b; --i) #define pii pair #define pll pair #define pb push_back #define eb emplace_back #define vi vector #define vll vector #define vpi vector #define vpll vector #define overload2(_1, _2, name, ...) name #define vec(type, name, ...) vector name(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define vv(type, name, h, ...) vector> name(h, vector(__VA_ARGS__)) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ IN(name) #define vvv(type, name, h, w, ...) vector>> name(h, vector>(w, vector(__VA_ARGS__))) #define fi first #define se second #define all(c) begin(c), end(c) #define ios ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) using namespace std; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define Size(c) (int)(c).size() #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define ULL(...) \ ull __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ IN(__VA_ARGS__) #define LD(...) \ ld __VA_ARGS__; \ IN(__VA_ARGS__) int scan() { return getchar(); } template void scan(T a) { cin >> a; } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template void scan(vector &); template void scan(array &); template void scan(pair &); template void scan(T (&)[size]); template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(deque &a) { for(auto &i : a) scan(i); } template void scan(array &a) { for(auto &i : a) scan(i); } template void scan(pair &p) { scan(p.first); scan(p.second); } template void scan(T (&a)[size]) { for(auto &i : a) scan(i); } template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &... tail) { scan(head); IN(tail...); } string stin() { string s; cin >> s; return s; } template inline bool chmax(T &a, S b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, S b) { if(a > b) { a = b; return 1; } return 0; } vi iota(int n) { vi a(n); iota(all(a), 0); return a; } template void UNIQUE(vector &x) { sort(all(x)); x.erase(unique(all(x)), x.end()); } int in() { int x; cin >> x; return x; } ll lin() { unsigned long long x; cin >> x; return x; } void print() { putchar(' '); } void print(bool a) { cout << a; } void print(int a) { cout << a; } void print(long long a) { cout << a; } void print(char a) { cout << a; } void print(string &a) { cout << a; } void print(double a) { cout << a; } template void print(const vector &); template void print(const array &); template void print(const pair &p); template void print(const T (&)[size]); template void print(const vector &a) { if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } cout << endl; } template void print(const deque &a) { if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } } template void print(const array &a) { print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } } template void print(const pair &p) { cout << '('; print(p.first); cout << ","; print(p.second); cout << ')'; } template void print(set &x) { for(auto e : x) print(e), cout << " "; cout << endl; } template void print(multiset &x) { for(auto e : x) print(e), cout << " "; cout << endl; } template void print(const T (&a)[size]) { print(a[0]); for(auto i = a; ++i != end(a);) { cout << " "; print(*i); } } template void print(const T &a) { cout << a; } int out() { putchar('\n'); return 0; } template int out(const T &t) { print(t); putchar('\n'); return 0; } template int out(const Head &head, const Tail &... tail) { print(head); putchar(' '); out(tail...); return 0; } ll gcd(ll a, ll b) { while(b) { ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b) { if(!a || !b) return 0; return a * b / gcd(a, b); } vector factor(ll x) { vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0) { ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(int x) { vector ans; for(int i = 1; i * i <= x; i++) if(x % i == 0) { ans.pb(i); if(i * i != x) ans.pb(x / i); } return ans; } template void zip(vector &x) { vector y = x; sort(all(y)); for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } } int popcount(ll x) { return __builtin_popcountll(x); } mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int rnd(int n) { return uniform_int_distribution(0, n - 1)(rng); } template void shuffle(vector &v) { rep3(i, v.size() - 1, 1) { swap(v[i], v[rnd(i)]); } } #define endl '\n' vector YES{"NO", "YES"}; vector Yes{"No", "Yes"}; vector yes{"no", "yes"}; #ifdef _LOCAL #undef endl #define debug(x) \ cout << #x << ": "; \ print(x); \ cout << endl; void err() {} template void err(const T &t) { print(t); cout << " "; } template void err(const Head &head, const Tail &... tail) { print(head); putchar(' '); out(tail...); } #else #define debug(x) template void err(const T &...) {} #endif template struct edge { int from, to; T cost; int id; edge(int to, T cost) : from(-1), to(to), cost(cost) {} edge(int from, int to, T cost) : from(from), to(to), cost(cost) {} // edge(int from,int to,T cost,int id):from(from),to(to),cost(cost),id(id){} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template using Edges = vector>; template using WeightedTree = vector>; template using Edges = vector>; template using WeightedGraph = vector>; template using Matrix = vector>; using Graph = vector>; using tree = vector>; tree getTree(int n, int offset = 1) { tree res(n); for(int i = 0; i < n - 1; i++) { int a, b; cin >> a >> b; a -= offset, b -= offset; res[a].emplace_back(b); res[b].emplace_back(a); } return res; } template WeightedTree getWeightedTree(int n, int offset = 1) { WeightedTree res(n); for(int i = 0; i < n - 1; i++) { int a, b; cin >> a >> b; a -= offset, b -= offset; T c; cin >> c; res[a].emplace_back(b, c); res[b].emplace_back(a, c); } return res; } Graph getGraph(int n, int m, int offset = 1) { Graph res(n); for(int i = 0; i < m; ++i) { int a, b; cin >> a >> b; a -= offset, b -= offset; res[a].emplace_back(b); res[b].emplace_back(a); } return res; } template WeightedGraph getWeightedGraph(int n, int m, int offset = 1) { WeightedGraph res(n); for(int i = 0; i < m; ++i) { int a, b; cin >> a >> b; T c; cin >> c; res[a].emplace_back(b, c); res[b].emplace_back(a, c); } } struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(15); } } setup_io; #pragma endregion // _________コーディングはここから!!___________ // namespace modular { // constexpr ll MOD = 998244353; // const int MAXN = 1100000; // template class modint { // using u64 = ll; // public: // u64 a; // constexpr modint(const u64 x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {} // constexpr u64 &value() noexcept { return a; } // constexpr const u64 &value() const noexcept { return a; } // 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; } // template constexpr modint operator^(T rhs) const noexcept { return modint(*this) ^= rhs; } // constexpr modint &operator+=(const modint rhs) noexcept { // a += rhs.a; // if(a >= Modulus) { a -= Modulus; } // return *this; // } // constexpr modint &operator-=(const modint rhs) noexcept { // if(a < rhs.a) { a += Modulus; } // a -= rhs.a; // return *this; // } // constexpr modint &operator*=(const modint rhs) noexcept { // a = a * rhs.a % Modulus; // return *this; // } // constexpr bool operator==(const modint rhs) const noexcept { return a == rhs.a; } // template constexpr modint &operator^=(T n) noexcept { // modint res = 1; // modint x = a; // while(n) { // if(n & 1) res *= x; // x *= x; // n >>= 1; // } // a = res.a; // return *this; // } // }; // #define mint modint // #define vmint vector // vmint Inv{0, 1}, Prd{1, 1}, Invprd{1, 1}; // mint inv(int n) { // if(Inv.size() > n) // return Inv[n]; // else { // for(int i = Inv.size(); i <= n; ++i) Inv.emplace_back(Inv[MOD % i] * (-MOD / i)); // return Inv[n]; // } // } // mint prd(int n) { // if(Prd.size() > n) // return Prd[n]; // else // for(int i = Prd.size(); i <= n; ++i) Prd.emplace_back(Prd[i - 1] * i); // return Prd[n]; // } // mint invprd(int n) { // if(Invprd.size() > n) // return Invprd[n]; // else // for(int i = Invprd.size(); i <= n; ++i) Invprd.emplace_back(Invprd[i - 1] * inv(i)); // return Invprd[n]; // } // mint modpow(ll a, ll n) { // mint x = a; // return x ^= n; // } // template modint operator/(modint l, modint r) { // if(r.a < MAXN) return l * inv(r.a); // return l * (r ^ (MOD - 2)); // } // template modint operator/(T l, modint r) { return modint(l) / r; } // template modint operator/=(modint &l, modint r) { return l = l / r; } // mint C(int a, int b) { // if(a < 0 || b < 0) return 0; // if(a < b) return 0; // return prd(a) * invprd(b) * invprd(a - b); // } // mint P(int a, int b) { // if(a < 0 || b < 0) return 0; // if(a < b) return 0; // return prd(a) * invprd(a - b); // } // ostream &operator<<(ostream &os, mint a) { // os << a.a; // return os; // } // template ostream &operator<<(ostream &os, vector &a) { // for(auto &e : a) os << e << " "; // os << endl; // return os; // } // istream &operator>>(istream &is, mint &a) { // ll x; // is >> x; // a = x; // return is; // } // } // namespace modular // Stirling number from https://judge.yosupo.jp/submission/4988 char readchar() { static char buf[1 << 15], *ptr = buf, *end = buf; if(ptr == end) ptr = buf, end = buf + fread(buf, 1, 1 << 15, stdin); return *ptr++; } void writechar(char c = 0) { static char buf[1 << 15], *ptr = buf; if(ptr == end(buf) or c == 0) fwrite(buf, 1, ptr - buf, stdout), ptr = buf; *ptr++ = c; } template Z getint() { char c = readchar(); bool neg = c == '-'; Z res = neg ? 0 : c - '0'; while(isdigit(c = readchar())) res = res * 10 + (c - '0'); return neg ? -res : res; } template void putint(Z a, char c = '\n') { if(a < 0) writechar('-'), a = -a; int d[40], i = 0; do d[i++] = a % 10; while(a /= 10); while(i--) writechar('0' + d[i]); writechar(c); } string getstring() { string res; for(char c; (c = readchar()) != '\n';) res += c; return res; } void putstring(string s) { for(char c : s) writechar(c); writechar('\n'); } template > T power(T a, long long n, Op op = multiplies(), T e = {1}) { assert(n >= 0); while(n) { if(n & 1) e = op(e, a); if(n >>= 1) a = op(a, a); } return e; } template struct modular { using m = modular; unsigned v; modular(long long x = 0) : v((x %= M) < 0 ? x + M : x) {} m operator-() const { return m() -= *this; } m &operator+=(m b) { if((v += b.v) >= M) v -= M; return *this; } m &operator-=(m b) { if(v < b.v) v += M; v -= b.v; return *this; } m &operator*=(m b) { v = (uint64_t)v * b.v % M; return *this; } m &operator/=(m b) { return *this *= power(b, M - 2); } friend m operator+(m a, m b) { return a += b; } friend m operator-(m a, m b) { return a -= b; } friend m operator*(m a, m b) { return a *= b; } friend m operator/(m a, m b) { return a /= b; } friend bool operator==(m a, m b) { return a.v == b.v; } friend string to_string(m a) { return to_string(a.v); } }; template void ntt(vector> &a, bool inverse) { static vector> dw(30), idw(30); if(dw[0] == 0) { modular root = 2; while(power(root, (M - 1) / 2) == 1) root += 1; for(int i = 0; i < 30; ++i) dw[i] = -power(root, (M - 1) >> (i + 2)), idw[i] = 1 / dw[i]; } int n = a.size(); assert((n & (n - 1)) == 0); if(not inverse) { for(int m = n; m >>= 1;) { modular w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; if(x.v >= M) x.v -= M; a[i].v = x.v + y.v, a[j].v = x.v + (M - y.v); } w *= dw[__builtin_ctz(++k)]; } } } else { for(int m = 1; m < n; m *= 2) { modular w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j].v = x.v + (M - y.v), a[j] *= w; } w *= idw[__builtin_ctz(++k)]; } } } auto c = 1 / modular(inverse ? n : 1); for(auto &&e : a) e *= c; } template vector> operator*(vector> a, vector> b) { if(a.empty() or b.empty()) return {}; int n = a.size(), m = b.size(), sz = 1 << __lg(2 * (n + m - 1) - 1); if(min(n, m) < 30) { vector res(n + m - 1); for(int i = 0; i < n; ++i) for(int j = 0; j < m; ++j) res[i + j] += (a[i] * b[j]).v; return {begin(res), end(res)}; } bool eq = a == b; a.resize(sz), ntt(a, false); if(eq) b = a; else b.resize(sz), ntt(b, false); for(int i = 0; i < sz; ++i) a[i] *= b[i]; ntt(a, true), a.resize(n + m - 1); return a; } constexpr long long mod = 998244353; using mint = modular; vector fact, inv_fact, minv; void prepare(int n) { fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1); for(int i = 0; i <= n; ++i) fact[i] = i ? i * fact[i - 1] : 1; inv_fact[n] = power(fact[n], mod - 2); for(int i = n; i; --i) inv_fact[i - 1] = i * inv_fact[i]; for(int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1]; } mint binom(int n, int k) { if(k < 0 or k > n) return 0; return fact[n] * inv_fact[k] * inv_fact[n - k]; } template <> mint &mint::operator/=(mint r) { return *this *= r.v < minv.size() ? minv[r.v] : power(r, mod - 2); } int main() { int n = getint(); int k = getint(); prepare(k + 1); vector a(k + 1), b(k + 1); for(int i = 0; i <= k; ++i) { a[i] = power(-1, i) * power(mint(i), n) * inv_fact[i]; b[i] = inv_fact[i]; } auto c = a * b; mint ans; for(int i = 1; i <= k; ++i) { c[i] *= power(-1, i); if((k - i) & 1) { ans += binom(k, i) * c[i].v * fact[i]; } // putint(c[i].v, " \n"[i == n]); } putint(ans.v, '\n'); writechar(); }