#include <bits/stdc++.h> using namespace std; #define all(v) (v).begin(),(v).end() #define pb(a) push_back(a) #define rep(i, n) for(int i=0;i<n;i++) #define foa(e, v) for(auto&& e : v) using ll = long long; const ll MOD7 = 1000000007, MOD998 = 998244353, INF = (1LL << 60); #define dout(a) cout<<fixed<<setprecision(10)<<a<<endl; template<int MOD> struct Modint { long long val; constexpr Modint(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int mod() const { return MOD; } constexpr long long value() const { return val; } constexpr Modint operator - () const noexcept { return val ? MOD - val : 0; } constexpr Modint operator + (const Modint& r) const noexcept { return Modint(*this) += r; } constexpr Modint operator - (const Modint& r) const noexcept { return Modint(*this) -= r; } constexpr Modint operator * (const Modint& r) const noexcept { return Modint(*this) *= r; } constexpr Modint operator / (const Modint& r) const noexcept { return Modint(*this) /= r; } constexpr Modint& operator += (const Modint& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Modint& operator -= (const Modint& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Modint& operator *= (const Modint& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Modint& operator /= (const Modint& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Modint& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Modint& r) const noexcept { return this->val != r.val; } friend constexpr istream& operator >> (istream& is, Modint<MOD>& x) noexcept { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream& os, const Modint<MOD>& x) noexcept { return os << x.val; } constexpr Modint<MOD> pow(long long n) noexcept { if (n == 0) return 1; if (n < 0) return this->pow(-n).inv(); Modint<MOD> ret = pow(n >> 1); ret *= ret; if (n & 1) ret *= *this; return ret; } constexpr Modint<MOD> inv() noexcept { long long a = this->val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return Modint<MOD>(u); } }; const int MOD = MOD998; using mint = Modint<MOD>; long long modinv(long long a, long long MOD) { long long b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } u %= MOD; if (u < 0) u += MOD; return u; } long long modpow(long long a, long long n, long long MOD) { long long res = 1; a %= MOD; if(n < 0) { n = -n; a = modinv(a, MOD); } while (n > 0) { if (n & 1) res = res * a % MOD; a = a * a % MOD; n >>= 1; } return res; } namespace NTT { int calc_primitive_root(int MOD) { if (MOD == 2) return 1; if (MOD == 167772161) return 3; if (MOD == 469762049) return 3; if (MOD == 754974721) return 11; if (MOD == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; long long x = (MOD - 1) >> 1; while (x % 2 == 0) x >>= 1; for (long long i = 3; i * i <= x; i += 2) { if (x % i == 0) { divs[cnt ++] = i; while (x % i == 0) x /= i; } } if (x > 1) divs[cnt++] = x; for (int g = 2;; ++ g) { bool ok = true; for (int i = 0; i < cnt; i++) { if (modpow(g, (MOD - 1) / divs[i], MOD) == 1) { ok = false; break; } } if (ok) return g; } } int get_fft_size(int N, int M) { int size_a = 1, size_b = 1; while (size_a < N) size_a <<= 1; while (size_b < M) size_b <<= 1; return std::max(size_a, size_b) << 1; } template<class mint> void trans(std::vector<mint>& v, bool inv = false) { if (v.empty()) return; int N = (int) v.size(); int MOD = v[0].mod(); int PR = calc_primitive_root(MOD); static bool first = true; static std::vector<long long> vbw(30), vibw(30); if (first) { first = false; for (int k = 0; k < 30; ++ k) { vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD); vibw[k] = modinv(vbw[k], MOD); } } for (int i = 0, j = 1; j < N - 1; ++ j) { for (int k = N >> 1; k > (i ^= k); k >>= 1); if (i > j) std::swap(v[i], v[j]); } for (int k = 0, t = 2; t <= N; ++ k, t <<= 1) { long long bw = vbw[k]; if (inv) bw = vibw[k]; for (int i = 0; i < N; i += t) { mint w = 1; for (int j = 0; j < (t >> 1); ++ j) { int j1 = i + j, j2 = i + j + (t >> 1); mint c1 = v[j1], c2 = v[j2] * w; v[j1] = c1 + c2; v[j2] = c1 - c2; w *= bw; } } } if (inv) { long long invN = modinv(N, MOD); for (int i = 0; i < N; ++ i) v[i] = v[i] * invN; } } static constexpr int MOD0 = 754974721; static constexpr int MOD1 = 167772161; static constexpr int MOD2 = 469762049; using mint0 = Modint<MOD0>; using mint1 = Modint<MOD1>; using mint2 = Modint<MOD2>; static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1); static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2); static const mint2 imod01 = 187290749; // imod1 / MOD0; // small case (T = mint, long long) template<class T> std::vector<T> naive_mul (const std::vector<T>& A, const std::vector<T>& B) { if (A.empty() || B.empty()) return {}; int N = (int) A.size(), M = (int) B.size(); std::vector<T> 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]; return res; } }; // mint template<class mint> std::vector<mint> convolution (const std::vector<mint>& A, const std::vector<mint>& B) { if (A.empty() || B.empty()) return {}; int N = (int) A.size(), M = (int) B.size(); if (std::min(N, M) < 30) return NTT::naive_mul(A, B); int MOD = A[0].mod(); int size_fft = NTT::get_fft_size(N, M); if (MOD == 998244353) { std::vector<mint> a(size_fft), b(size_fft), c(size_fft); for (int i = 0; i < N; ++i) a[i] = A[i]; for (int i = 0; i < M; ++i) b[i] = B[i]; NTT::trans(a), NTT::trans(b); std::vector<mint> res(size_fft); for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i]; NTT::trans(res, true); res.resize(N + M - 1); return res; } std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0); std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0); std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0); for (int i = 0; i < N; ++ i) { a0[i] = A[i].value(); a1[i] = A[i].value(); a2[i] = A[i].value(); } for (int i = 0; i < M; ++ i) { b0[i] = B[i].value(); b1[i] = B[i].value(); b2[i] = B[i].value(); } NTT::trans(a0), NTT::trans(a1), NTT::trans(a2), NTT::trans(b0), NTT::trans(b1), NTT::trans(b2); for (int i = 0; i < size_fft; ++i) { c0[i] = a0[i] * b0[i]; c1[i] = a1[i] * b1[i]; c2[i] = a2[i] * b2[i]; } NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true); static const mint mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1; std::vector<mint> res(N + M - 1); for (int i = 0; i < N + M - 1; ++ i) { int y0 = c0[i].value(); int y1 = (NTT::imod0 * (c1[i] - y0)).value(); int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value(); res[i] = mod01 * y2 + mod0 * y1 + y0; } return res; } // long long std::vector<long long> convolution_ll (const std::vector<long long>& A, const std::vector<long long>& B) { if (A.empty() || B.empty()) return {}; int N = (int) A.size(), M = (int) B.size(); if (std::min(N, M) < 30) return NTT::naive_mul(A, B); int size_fft = NTT::get_fft_size(N, M); std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0); std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0); std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0); for (int i = 0; i < N; ++ i) { a0[i] = A[i]; a1[i] = A[i]; a2[i] = A[i]; } for (int i = 0; i < M; ++ i) { b0[i] = B[i]; b1[i] = B[i]; b2[i] = B[i]; } NTT::trans(a0), NTT::trans(a1), NTT::trans(a2), NTT::trans(b0), NTT::trans(b1), NTT::trans(b2); for (int i = 0; i < size_fft; ++ i) { c0[i] = a0[i] * b0[i]; c1[i] = a1[i] * b1[i]; c2[i] = a2[i] * b2[i]; } NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true); static const long long mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1; static const __int128_t mod012 = (__int128_t)mod01 * NTT::MOD2; std::vector<long long> res(N + M - 1); for (int i = 0; i < N + M - 1; ++ i) { int y0 = c0[i].value(); int y1 = (NTT::imod0 * (c1[i] - y0)).value(); int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value(); __int128_t tmp = (__int128_t)mod01 * y2 + (__int128_t)mod0 * y1 + y0; if(tmp < (mod012 >> 1)) res[i] = tmp; else res[i] = tmp - mod012; } return res; } // depends on {modint.cpp} int main() { cin.tie(0); ios::sync_with_stdio(false); ll n, k; cin >> n >> k; vector<mint> a(6, 0); a[0] = 1; vector<mint> b(6, 1); mint inv = mint(6).pow(-n); while(n) { if(n & 1) { a = convolution(a, b); for(int j = 6; j <= 10; j ++) a[j - 6] += a[j]; a.resize(6); } b = convolution(b, b); for(int j = 6; j <= 10; j ++) b[j - 6] += b[j]; b.resize(6); n >>= 1; } cout << a[k] * inv << endl; return 0; }