#include <bits/stdc++.h>
// #include <boost/multiprecision/cpp_int.hpp>
// using i128 = boost::multiprecision::int128_t;
#define _GLIBCXX_DEBUG
using namespace std;
using ll = long long;
using ld = long double;
using V = vector<int>;
using Vll = vector<ll>;
using Vld = vector<ld>;
using Vbo = vector<bool>;
using VV = vector<V>;
using VVll = vector<Vll>;
using VVld = vector<Vld>;
using VVbo = vector<Vbo>;
using VVV = vector<VV>;
using VVVll = vector<VVll>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using Pld = pair<ld, ld>;
#define rep2(i, m, n) for(int i=int(m); i<int(n); ++i)
#define drep2(i, m, n) for(int i=int(m)-1; i>=int(n); --i)
#define rep(i, n) rep2(i, 0, n)
#define drep(i, n) drep2(i, n, 0)
#define all(a) a.begin(), a.end()
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
template<typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; }
template<typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p) { is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << " "; return os; }
template<typename T> inline int count_between(vector<T> &a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r)
inline int Log2(ll x) { int k; for (k = 0; x > 0; ++k) x >>= 1; return k; } // number of binary digits
const int INF  = 1<<30;
const ll INFll = 1ll<<62;
const ld EPS   = 1e-10;
const ld PI    = acos(-1.0);
// const int MOD  = int(1e9)+7;
const int MOD  = 998244353;


struct mint {
  ll x;
  mint(ll x=0) : x((x%MOD+MOD)%MOD) {}
  mint operator-() const { return mint(-x);}
  mint& operator+=(const mint a) { if ((x += a.x) >= MOD) x -= MOD; return *this; }
  mint& operator-=(const mint a) { if ((x -= a.x) < 0) x += MOD; return *this; }
  mint& operator*=(const mint a) { (x *= a.x) %= MOD; return *this;}
  mint operator+(const mint a) const { return mint(*this) += a;}
  mint operator-(const mint a) const { return mint(*this) -= a;}
  mint operator*(const mint a) const { return mint(*this) *= a;}
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }
  mint& operator/=(const mint r) {
    ll a = r.x, b = MOD, u = 1, v = 0;
    while (b) {
      ll t = a / b;
      a -= t * b; swap(a, b);
      u -= t * v; swap(u, v);
    }
    x = x * u % MOD;
    if (x < 0) x += MOD;
    return *this;
  }
  mint operator/(const mint a) const { return mint(*this) /= a;}
};
// istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}
using Vm = vector<mint>;
using VVm = vector<Vm>;
using VVVm = vector<VVm>;


template<typename T>
struct Polynomial : vector<T> {
  using vector<T>::vector;
  using P = Polynomial;
  int n = (*this).size();
  P operator-() const {
    P res(n);
    rep(i, n) res[i] = -(*this)[i];
    return res;
  }
  P &operator+=(const P q) {
    rep(i, n) if (i < q.size()) (*this)[i] += q[i];
    return *this;
  }
  P &operator-=(const P q) {
    rep(i, n) if (i < q.size()) (*this)[i] -= q[i];
    return *this;
  }
  P &operator*=(const P q) { // dense
    drep(i, n) {
      (*this)[i] *= q[0];
      rep2(j, 1, int(q.size())) if (j <= i) (*this)[i] += (*this)[i-j] * q[j];
    }
    return *this;
  }
  template<typename T2>
  P &operator*=(map<int, T2> q) { // sparse
    drep(i, n) {
      (*this)[i] *= q[0];
      for (auto &[j, b] : q) if (j > 0 && j <= i) (*this)[i] += (*this)[i-j] * b;
    }
    return *this;
  }
  P &operator/=(const P q) { // dense
    rep(i, n) {
      rep2(j, 1, int(q.size())) if (j <= i) (*this)[i] -= (*this)[i-j] * q[j];
      (*this)[i] /= q[0];
    }
    return *this;
  }
  template<typename T2>
  P &operator/=(map<int, T2> q) { // sparse
    rep(i, n) {
      for (auto &[j, b] : q) if (j > 0 && j <= i) (*this)[i] -= (*this)[i-j] * b;
      (*this)[i] /= q[0];
    }
    return *this;
  }
  template<typename T2> P operator+(const T2 q) const { return P(*this) += q; }
  template<typename T2> P operator-(const T2 q) const { return P(*this) -= q; }
  template<typename T2> P operator*(const T2 q) const { return P(*this) *= q; }
  template<typename T2> P operator/(const T2 q) const { return P(*this) /= q; }
};
using Pol = Polynomial<mint>;
using Pol2 = Polynomial<Pol>;


int main() {
  string s; cin >> s;
  int K; cin >> K;

  V a(1);
  for (auto c : s) {
    if (c == '0') a.push_back(0);
    if (c == '1') a.back()++;
  }
  int n = a.size();
  auto b = a;
  rep(i, n-1) b[i+1] += b[i];
  int m = b[n-1];

  Pol2 dp(m+1, Pol(m+1));
  dp[0][0] = 1;

  rep(i, n) {
    map<int, map<int, mint>> q1, q2, q3, q4;

    q1[0][0] = 1;
    q1[a[i]][0] += -1;

    q2[0][0] = 1;
    q2[1][0] = -1;

    q3[a[i]][0] = 1;
    
    q4[0][0] = 1;
    q4[1][1] = -1;
    
    dp = dp*q1/q2 + dp*q3/q4;
    rep(j, b[i]) dp[j] = Pol(m+1);
  }

  chmin(K, m);
  mint ans = 0;
  rep(k, K+1) ans += dp[m][k];
  cout << ans << "\n";
  return 0;
}


Measured memory_bytes: 9096