#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; double EPS = 1e-15; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif //【数字和】O(log n) /* * 非負の数 n を b 進表記したときの桁の数字の和を返す. * * 制約:b >= 2 */ ll digit_sum(ll n, ll b = 10) { // verify : https://atcoder.jp/contests/abc080/tasks/abc080_b Assert(b >= 2); ll sum = 0; while (n > 0) { sum += n % b; n /= b; } return sum; } mint naive(int n, int k) { mint res = 0; rep(i, pow(10, n)) { if (i % 99 == 0) { int d = digit_sum(i); res += mint(d).pow(k); } } return res; } mint TLE(int n, int k) { int hn = n / 2; int m = 11; int L = 1; vvm dp(m, vm(L)); dp[0][0] = 1; int L2 = 18 + 1; vvm pow2(m, vm(L2)); rep(d0, 10) rep(d1, 10) { pow2[(10 * d1 + d0) % m][d1 + d0]++; } while (hn > 0) { if (hn & 1) { int nL = L + L2 - 1; vvm ndp(m, vm(nL)); rep(k1, m) rep(k2, m) { auto c = convolution(dp[k1], pow2[k2]); rep(j, nL) ndp[(k1 + k2) % m][j] += c[j]; } dp = move(ndp); L = nL; } int nL2 = 2 * L2 - 1; vvm npow2(m, vm(nL2)); rep(k1, m) rep(k2, m) { auto c = convolution(pow2[k1], pow2[k2]); rep(j, nL2) npow2[(k1 + k2) % m][j] += c[j]; } pow2 = move(npow2); L2 = nL2; hn /= 2; } dumpel(dp); if (n & 1) { int nL = L + 10 - 1; vvm ndp(m, vm(nL)); rep(k1, m) rep(j, L) rep(j2, 10) { ndp[(k1 + j2) % m][j + j2] += dp[k1][j]; } dp = move(ndp); L = nL; } dumpel(dp); mint res = 0; rep(j, L) { if (j % 9 != 0) continue; res += dp[0][j] * mint(j).pow(k); } return res; } mint solve(int n, int K) { int hn = n / 2; int m = 11; int L = 1; vvm dp(m, vm(L)); dp[0][0] = 1; int L2 = 18 + 1; vvm pow2(m, vm(L2)); rep(d0, 10) rep(d1, 10) { pow2[(10 * d1 + d0) % m][d1 + d0]++; } while (hn > 0) { int W = 1 << (msb(L2 + L2 - 2) + 1); mint W_inv = mint(W).inv(); vvm pow2T(pow2); rep(k, m) { pow2T[k].resize(W); internal::butterfly(pow2T[k]); } if (hn & 1) { vvm dpT(dp); rep(k, m) { dpT[k].resize(W); internal::butterfly(dpT[k]); } dp = vvm(m, vm(W)); rep(k1, m) rep(k2, m) { rep(j, W) dp[(k1 + k2) % m][j] += dpT[k1][j] * pow2T[k2][j]; } L = L + L2 - 1; rep(k, m) { internal::butterfly_inv(dp[k]); dp[k].resize(L); rep(j, L) dp[k][j] *= W_inv; } } pow2 = vvm(m, vm(W)); rep(k, m) rep(j, W) { pow2[(2 * k) % m][j] += pow2T[k][j] * pow2T[k][j]; } rep(k1, m) repi(k2, k1 + 1, m - 1) { rep(j, W) pow2[(k1 + k2) % m][j] += 2 * pow2T[k1][j] * pow2T[k2][j]; } L2 = 2 * L2 - 1; rep(k, m) { internal::butterfly_inv(pow2[k]); pow2[k].resize(L2); rep(j, L2) pow2[k][j] *= W_inv; } hn /= 2; } dumpel(dp); if (n & 1) { int nL = L + 10 - 1; vvm ndp(m, vm(nL)); rep(k1, m) rep(j, L) rep(j2, 10) { ndp[(k1 + j2) % m][j + j2] += dp[k1][j]; } dp = move(ndp); L = nL; } dumpel(dp); mint res = 0; rep(j, L) { if (j % 9 != 0) continue; res += dp[0][j] * mint(j).pow(K); } res; return res; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); int n, k; cin >> n >> k; dump(n, k); dump("-----"); dump(naive(n, k)); dump("-----"); auto res = solve(n, k); cout << res << endl; }