#include using namespace std; //* ATCODER #include using namespace atcoder; typedef modint998244353 mint; //*/ /* BOOST MULTIPRECISION #include using namespace boost::multiprecision; //*/ typedef long long ll; #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) template bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } template T max(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]); return ret; } template T min(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]); return ret; } template T sum(vector &a){ T ret = 0; for (int i=0; i<(int)a.size(); i++) ret += a[i]; return ret; } //defmodfact const int COMinitMAX = 4000000; mint fact[COMinitMAX+1], factinv[COMinitMAX+1]; void modfact(){ fact[0] = 1; for (int i=1; i<=COMinitMAX; i++){ fact[i] = fact[i-1] * i; } factinv[COMinitMAX] = fact[COMinitMAX].inv(); for (int i=COMinitMAX-1; i>=0; i--){ factinv[i] = factinv[i+1] * (i+1); } } mint cmb(int a, int b){ if (a poly_inv(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); mint r = a[0].pow((ll)(mint::mod())-2); int m = 1; vector res = {r}; while (m < M){ vector f = a; f.resize(2 * m); vector g = res; g.resize(2 * m); internal::butterfly(f); internal::butterfly(g); for (int i=0; i<2*m; i++){ f[i] = f[i] * g[i]; } internal::butterfly_inv(f); for (int i=0; i poly_log(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); if (n == 1) return vector(M, 0); vector b(n-1); for (int i=0; i t = convolution(b, poly_inv(a, M)); vector ret(M); for (int i=0; i poly_exp(vector &a, int M = -314159265){ if (M == -314159265) M = (int)a.size(); else if (M <= 0) return {}; int n = a.size(); int m = 1; vector res = {1}; while (m < M){ vector f(2*m); for (int i=0; i v = poly_log(res, 2*m); vector w(2*m); for (int i=0; i<2*m; i++) w[i] = f[i] - v[i]; w[0] += 1; vector g = convolution(res, w); res.insert(res.end(), g.begin()+m, g.begin()+2*m); m <<= 1; } res.resize(M); return res; } vector poly_pow_nonzero(vector &a, ll m, ll l){ int n = a.size(); mint bais = a[0].pow(m); mint invs; if (a[0].val() == 0) invs = 0; else invs = a[0].inv(); vector r(n); for (int i=0; i poly_pow(vector &a, ll m, ll l){ int n = a.size(); int ind = 0; for (int i=0; i= l){ return vector(l, 0); } vector ret(g*ind); vector b(n-ind); for (int i=0; i tmp; if (l-g*ind > 0) tmp = poly_pow_nonzero(b, m, l-g*ind); else tmp = {}; ret.insert(ret.end(), tmp.begin(), tmp.end()); return ret; } int main(){ modfact(); int n, k; cin >> n >> k; vector g(10); rep(i,0,10){ g[i] = 1; } vector f1 = poly_pow(g, n/2, 500001); vector f2 = poly_pow(g, (n+1)/2, 500001); vector> v1(11, vector(500001)); vector> v2(11, vector(500001)); rep(i,0,500001){ v1[(10*i)%11][i] = f1[i]; v2[i%11][i] = f2[i]; } vector tmp(1000001); rep(j,0,11){ vector v = convolution(v1[j], v2[(11-j)%11]); rep(i,0,1000001){ tmp[i] += v[i]; } } mint ans = 0; for (int i=1; i<(int)tmp.size(); i++){ if (i % 9 == 0){ ans += mint(i).pow(k) * tmp[i]; } } cout << ans.val() << '\n'; }