#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; template struct Mat : array, N> { using M = Mat; void make_identity() { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = zero(); } } for (int i = 0; i < N; i++) { (*this)[i][i] = one(); } } M& operator+=(const M& rhs) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = add((*this)[i][j], rhs[i][j]); } } return *this; } M& operator*=(const M& rhs) { static M temp; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { temp[i][j] = zero(); } } for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { for (int k = 0; k < N; k++) { temp[i][k] = add(temp[i][k], mul((*this)[i][j], rhs[j][k])); } } } *this = temp; return *this; } template void inplace_pow(I k) { assert(k >= 0); static M temp; temp = *this; make_identity(); while (k) { if (k & 1) *this *= temp; k >>= 1; if (k) temp *= temp; } } friend ostream& operator<<(ostream& os, const M& A) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { os << A[i][j] << " \n"[j + 1 == N]; } } return os; } }; // mint mint add0(mint x, mint y) { return x + y; } mint zero0() { return mint(); } mint mul0(mint x, mint y) { return x * y; } mint one0() { return mint::raw(1); } using M0 = Mat; M0 add(M0 x, M0 y) { x += y; return x; } M0 zero() { return M0{}; } M0 mul(M0 x, M0 y) { x *= y; return x; } M0 one() { M0 z; z.make_identity(); return z; } using M = Mat; } int main() { ios::sync_with_stdio(false); cin.tie(0); string s; int k; cin >> s >> k; int n = s.size(); M m; rep(u, 10) { int i = 0; while (i < n && s[i] - '0' != u) i++; if (i == n) { m[u][u] = one(); continue; } int last[10]{}; last[u] = i; static vector acc; acc.assign(n + 1, M0{}); acc[i+1][0][0] = 1; acc[i+1][0][1] = u; acc[i+1][1][0] = 0; acc[i+1][1][1] = 10; for (i++; i < n; i++) { int x = s[i] - '0'; M0 t = acc[i]; rep(i, 2) rep(j, 2) t[i][j] -= acc[last[x]][i][j]; M0 tt; tt[0][0] = 1; tt[0][1] = x; tt[1][0] = 0; tt[1][1] = 10; t *= tt; acc[i+1] = acc[i]; acc[i+1] += t; last[x] = i; } rep(v, 10) { M0 t = acc[n]; rep(i, 2) rep(j, 2) t[i][j] -= acc[last[v]][i][j]; m[u][v] = t; } m[u][10] += acc[n]; } m[10][10].make_identity(); m.inplace_pow(k); mint ans; rep(u, 10) if (u) ans += m[u][10][0][1]; cout << ans.val() << '\n'; }