#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
//const int mod = (int) (1e9 + 7);
const int mod = 998244353;

const int64 infll = (1LL << 60) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

int main() {

  string S;
  int K;
  cin >> S >> K;
  int N = (int) S.size();
  chmin(K, N);


  vector< pair< int, int > > st;
  for(int i = 0; i < N; i++) {
    if(st.empty() || st.back().first != S[i] || S[i] == '0') {
      st.emplace_back(S[i], 0);
    }
    st.back().second++;
  }

  auto dp = make_v< modint >(K + 1, K + 1);
  dp[0][0] = 1;
  vector< int > sum(st.size() + 1);
  for(int i = (int) st.size() - 1; i >= 0; i--) {
    sum[i] = sum[i + 1];
    if(st[i].first == '1') sum[i] += st[i].second;
    chmin(sum[i], K);
  }

  for(int i = 0; i < st.size(); i++) {
    auto dp2 = make_v< modint >(K + 1, K + 1);
    if(i + 1 < st.size() && st[i].first == '1' && st[i + 1].first == '0') {
      for(int j = 0; j <= sum[i]; j++) {
        for(int k = j; k <= K; k++) {
          for(int l = 0; l <= st[i].second && j - l >= 0; l++) { // 減らす or 変えない
            dp2[k][j - l] += dp[k][j];
          }
          for(int l = 1; j + l <= sum[i + 1] && k + l <= K; l++) {
            dp2[k + l][j + l] += dp[k][j];
          }
        }
      }
      ++i;
    } else if(st[i].first == '0') {
      for(int j = 0; j <= sum[i]; j++) {
        for(int k = j; k <= K; k++) {
          for(int l = 0; j + l <= sum[i] && k + l <= K; l++) {
            dp2[k + l][j + l] += dp[k][j];
          }
        }
      }
    } else {
      for(int k = 0; k <= K; k++) {
        for(int j = 0; j <= sum[i]; j++) {
          dp2[k][max(0, j - st[i].second)] += dp[k][j];
          if(j + 1 <= K) dp2[k][j + 1] -= dp[k][j];
        }
        for(int j = 1; j <= K; j++) {
          dp2[k][j] += dp2[k][j - 1];
        }
      }
    }
    dp.swap(dp2);
  }

  modint ret = 0;
  for(int i = 0; i <= K; i++) ret += dp[i][0];
  cout << ret << "\n";
}







Measured memory_bytes: 3960