// Begin include: "../../template/template.hpp" using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility // Begin include: "util.hpp" namespace yamada { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; using lld = long double; template using V = vector; template using VV = vector>; template using VVV = vector>>; template using VVVV = vector>>>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; using vvvl = vector>>; using vvvvl = vector>>>; template using minpq = priority_queue, greater>; template using maxpq = priority_queue, less>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; using vvp = VV; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), T(0)); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(T &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } template vector Digit(T a, const U &x) { vector ret; while (a > 0) { ret.emplace_back(a % x); a /= x; } return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; if(v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } template T bisect(T ok, T bad, F pred) { if (ok == bad) return ok; if (!pred(ok)) return ok; while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template T bisect_double(T ok, T bad, F pred, int iter = 100) { if (ok == bad) return ok; if (!pred(ok)) return ok; for (int i = 0; i < iter; i++){ T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } return bad; } template bool inLR(T L, T x, T R){ return (L <= x && x < R); } bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; } bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; } template void mout(mint a, int M = 100) { if (a == 0) { cout << 0 << "\n"; return; } for (int i = 0; i <= M; i++) for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == a) { if (j == 1) cout << i << "\n"; else cout << i << "/" << j << "\n"; return; } else if (val == -a) { if (j == 1) cout << -i << "\n"; else cout << -i << "/" << j << "\n"; return; } } cout << "NF\n"; } template void mout(std::vector A, int M = 100) { int N = A.size(); for (int pos = 0; pos < N; pos++) { if (A[pos] == 0) { cout << 0 << (pos == N - 1 ? "\n" : " "); continue; } bool fn = false; for (int i = 0; i <= M; i++) { for (int j = 1; j <= M; j++) { mint val = (mint)i / j; if (val == A[pos]) { if (j == 1) cout << i << (pos == N - 1 ? "\n" : " "); else cout << i << "/" << j << (pos == N - 1 ? "\n" : " "); fn = true; break; } else if (val == -A[pos]) { if (j == 1) cout << -i << (pos == N - 1 ? "\n" : " "); else cout << -i << "/" << j << (pos == N - 1 ? "\n" : " "); fn = true; break; } } if (fn) break; } if (!fn) cout << "NF" << (pos == N - 1 ? "\n" : " "); } } } // namespace yamada // End include: "util.hpp" // bit operation // Begin include: "bitop.hpp" namespace yamada { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return __builtin_popcountll(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace yamada // End include: "bitop.hpp" // inout // Begin include: "inout.hpp" namespace yamada { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupYamada { IoSetupYamada() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupyamada; } // namespace yamada // End include: "inout.hpp" // macro // Begin include: "macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define each3(x, y, z, v) for (auto&& [x, y, z] : v) #define all(v) (v).begin(), (v).end() #define rep1(a) for (long long i = 0; i < (long long)(a); ++i) #define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i) #define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i) #define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i) #define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i) #define overload3(a, b, c, d, ...) d #define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__) #define eb emplace_back #define mkp make_pair #define mkt make_tuple #define fi first #define se second #define vv(type, name, h, ...) \ vector > name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ yamada::out(__VA_ARGS__);\ return; \ } while (0) // End include: "macro.hpp" namespace yamada { void solve(); } int main() { yamada::solve(); } // End include: "../../template/template.hpp" // Begin include: "../../modint/montgomery-modint.hpp" template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; // End include: "../../modint/montgomery-modint.hpp" using mint = LazyMontgomeryModInt<998244353>; void yamada::solve() { auto query=[&](ll N,ll K)->mint{ VVdp(N+1,V(K+1)); dp[0][0]=1; rep(i,N)rep(j,K+1)if(dp[i][j]!=0){ if(j0)dp[i+1][j-1]+=dp[i][j]; } return dp[N][0]; }; inl(N,K); N*=2; mint ans=query(N,K); ans-=query(N,K-1); out(ans); }