#include #include using namespace std; using namespace atcoder; struct Fast { Fast() { std::cin.tie(nullptr); ios::sync_with_stdio(false); cout << setprecision(10); } } fast; #define popcount(x) __builtin_popcount(x) #define all(a) (a).begin(), (a).end() #define contains(a, x) ((a).find(x) != (a).end()) #define rep(i, a, b) for (int i = (a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b)-1; i >= (a); i--) #define writejoin(s, a) rep(_i, 0, (a).size()) cout << (a)[_i] << (_i + 1 < (int)(a).size() ? s : "\n"); #define YN(b) cout << ((b) ? "YES" : "NO") << "\n"; #define Yn(b) cout << ((b) ? "Yes" : "No") << "\n"; #define yn(b) cout << ((b) ? "yes" : "no") << "\n"; using ll = long long; using mint = modint998244353; template class Factorial { public: Factorial(int max) : n(max) { f = vector(n + 1); finv = vector(n + 1); f[0] = 1; for (int i = 1; i <= n; i++) f[i] = f[i - 1] * i; finv[n] = f[n].inv(); for (int i = n; i > 0; i--) finv[i - 1] = finv[i] * i; } mint fact(int k) { assert(0 <= k && k <= n); return f[k]; } mint fact_inv(int k) { assert(0 <= k && k <= n); return finv[k]; } mint binom(int k, int r) { assert(0 <= k && k <= n); if (r < 0 || r > k) return 0; return f[k] * finv[r] * finv[k - r]; } mint inv(int k) { assert(0 < k && k <= n); return finv[k] * f[k - 1]; } private: int n; vector f, finv; }; template struct FormalPowerSeries : vector { using vector::vector; using FPS = FormalPowerSeries; FPS &operator+=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i]; return *this; } FPS &operator+=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] += r; return *this; } FPS &operator-=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; return *this; } FPS &operator-=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] -= r; return *this; } FPS &operator*=(const mint &v) { for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v; return *this; } FPS &operator*=(const FPS &r) { auto c = convolution((*this), r); this->resize(c.size()); for (int i = 0; i < (int)c.size(); i++) (*this)[i] = c[i]; return *this; } FPS &operator/=(const FPS &r) { if (this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; if ((int)r.size() <= 64) { FPS f(*this), g(r); g.shrink(); mint coeff = g.at(g.size() - 1).inv(); for (auto &x : g) x *= coeff; int deg = (int)f.size() - (int)g.size() + 1; int gs = g.size(); FPS quo(deg); for (int i = deg - 1; i >= 0; i--) { quo[i] = f[i + gs - 1]; for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j]; } *this = quo * coeff; this->resize(n, mint(0)); return *this; } return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev(); } FPS &operator%=(const FPS &r) { *this -= *this / r * r; shrink(); return *this; } FPS operator+(const FPS &r) const { return FPS(*this) += r; } FPS operator+(const mint &v) const { return FPS(*this) += v; } FPS operator-(const FPS &r) const { return FPS(*this) -= r; } FPS operator-(const mint &v) const { return FPS(*this) -= v; } FPS operator*(const FPS &r) const { return FPS(*this) *= r; } FPS operator*(const mint &v) const { return FPS(*this) *= v; } FPS operator/(const FPS &r) const { return FPS(*this) /= r; } FPS operator%(const FPS &r) const { return FPS(*this) %= r; } FPS operator-() const { FPS ret(this->size()); for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i]; return ret; } void shrink() { while (this->size() && this->back() == mint(0)) this->pop_back(); } FPS rev() const { FPS ret(*this); reverse(begin(ret), end(ret)); return ret; } FPS dot(FPS r) const { FPS ret(min(this->size(), r.size())); for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } FPS pre(int sz) const { return FPS(begin(*this), begin(*this) + min((int)this->size(), sz)); } FPS operator>>(int sz) const { if ((int)this->size() <= sz) return {}; FPS ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } FPS operator<<(int sz) const { FPS ret(*this); ret.insert(ret.begin(), sz, mint(0)); return ret; } FPS diff() const { const int n = (int)this->size(); FPS ret(max(0, n - 1)); mint one(1), coeff(1); for (int i = 1; i < n; i++) { ret[i - 1] = (*this)[i] * coeff; coeff += one; } return ret; } FPS integral() const { const int n = (int)this->size(); FPS ret(n + 1); ret[0] = mint(0); if (n > 0) ret[1] = mint(1); auto mod = mint::get_mod(); for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i); for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i]; return ret; } mint eval(mint x) const { mint r = 0, w = 1; for (auto &v : *this) r += w * v, w *= x; return r; } FPS log(int deg = -1) const { assert((*this)[0] == mint(1)); if (deg == -1) deg = (int)this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } FPS pow(int64_t k, int deg = -1) const { const int n = (int)this->size(); if (deg == -1) deg = n; if (k == 0) { FPS ret(deg); if (deg) ret[0] = 1; return ret; } for (int i = 0; i < n; i++) { if ((*this)[i] != mint(0)) { mint rev = mint(1) / (*this)[i]; FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg); ret *= (*this)[i].pow(k); ret = (ret << (i * k)).pre(deg); if ((int)ret.size() < deg) ret.resize(deg, mint(0)); return ret; } if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0)); } return FPS(deg, mint(0)); } FPS inv(int deg = -1) const { assert((*this)[0] != mint(0)); if (deg == -1) deg = (*this).size(); FPS ret{mint(1) / (*this)[0]}; for (int i = 1; i < deg; i <<= 1) ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1); return ret.pre(deg); } FPS exp(int deg = -1) const { assert((*this)[0] == mint(0)); if (deg == -1) deg = (*this).size(); FPS ret{mint(1)}; for (int i = 1; i < deg; i <<= 1) ret = (ret * ((*this).pre(i << 1) - ret.log(i << 1) + 1)).pre(i << 1); return ret.pre(deg); } }; vector mul(const vector &f, const vector &g) { auto h = convolution(f, g); rrep(i, 99, h.size()) h[i - 99] += h[i]; if ((int)h.size() > 99) h.resize(99); return h; } using fps = FormalPowerSeries; fps prod(const vector> &f, const int deg) { if ((int)f.size() == 0) return fps{0}; queue q1, q2; for (auto e : f) { q1.push(fps{e.first}); q2.push(fps{1, -e.second}); } while (q1.size() > 1) { auto u1 = q1.front(); q1.pop(); auto u2 = q1.front(); q1.pop(); auto v1 = q2.front(); q2.pop(); auto v2 = q2.front(); q2.pop(); q1.push(u1 * v2 + u2 * v1); q2.push(v1 * v2); } return q1.front() * q2.front().inv(deg); } int main() { int n, k; cin >> n >> k; Factorial fact(100000); vector f{1}, g{1}; vector a(10, 1); int mf = n / 2; int mg = (n + 1) / 2; while (mg) { if (mf & 1) f = convolution(f, a); if (mg & 1) g = convolution(g, a); a = convolution(a, a); mf /= 2; mg /= 2; } using P = pair; vector> fr(99, vector(k + 1)), gr(99, vector(k + 1)); rep(r, 0, 99) { vector

fs, gs; for (int v = r; v < (int)f.size(); v += 99) fs.push_back(P{f[v], v}); for (int v = r; v < (int)g.size(); v += 99) gs.push_back(P{g[v], v}); fr[r] = prod(fs, k + 1); fr[r].resize(k + 1); gr[r] = prod(gs, k + 1); gr[r].resize(k + 1); } mint ans = 0; rep(i, 0, k + 1) rep(v, 0, 99) ans += fact.binom(k, i) * fr[v][i] * gr[(99 - v) * 10 % 99][k - i]; cout << ans.val() << "\n"; }