#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>

template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { lhs = rhs; return true; }
  return false;
}

template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { lhs = rhs; return true; }
  return false;
}

struct range {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_) noexcept : i(i_) { }
    constexpr void operator ++ () noexcept { ++i; }
    constexpr itr operator * () const noexcept { return i; }
    constexpr bool operator != (iterator x) const noexcept { return i != x.i; }
  };
  const iterator l, r;
  constexpr range(itr l_, itr r_) noexcept : l(l_), r(std::max(l_, r_)) { }
  constexpr iterator begin() const noexcept { return l; }
  constexpr iterator end() const noexcept { return r; }
};

struct revrange {
  using itr = int64_t;
  struct iterator {
    itr i;
    constexpr iterator(itr i_) noexcept : i(i_) { }
    constexpr void operator ++ () noexcept { --i; }
    constexpr itr operator * () const noexcept { return i; }
    constexpr bool operator != (iterator x) const noexcept { return i != x.i; }
  };
  const iterator l, r;
  constexpr revrange(itr l_, itr r_) noexcept : l(l_ - 1), r(std::max(l_, r_) - 1) { }
  constexpr iterator begin() const noexcept { return r; }
  constexpr iterator end() const noexcept { return l; }
};

template <uint32_t Modulus>
class modular {
public:
  using value_type = uint32_t;
  using max_type = uint64_t;

  static constexpr value_type mod = Modulus;
  static constexpr value_type get_mod() { return mod; }
  static_assert(mod >= 2, "invalid mod :: smaller than 2");
  static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31");

  template <class T>
  static constexpr value_type normalize(T value_) {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod;
      if (value_ == 0) return 0;
      return mod - value_;
    }
    return value_ % mod;
  }

private:
  value_type value;

public:
  constexpr modular(): value(0) { }
  template <class T>
  explicit constexpr modular(T value_): value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() { return static_cast<T>(value); }

  constexpr value_type get() const { return value; }
  constexpr modular operator - () const { return modular(mod - value); }
  constexpr modular operator ~ () const { return inverse(); }

  constexpr value_type &extract() { return value; }
  constexpr modular inverse() const { return power(mod - 2); }
  constexpr modular power(max_type exp) const {
    modular res(1), mult(*this);
    while (exp > 0) {
      if (exp & 1) res *= mult;
      mult *= mult;
      exp >>= 1;
    }
    return res;
  }

  constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) { 
    if ((value += rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) { 
    if ((value += mod - rhs.value) >= mod) value -= mod; 
    return *this; 
  }

  constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) { 
    value = (max_type) value * rhs.value % mod;
    return *this;
  }

  constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); }

  constexpr bool zero() const { return value == 0; }
  constexpr bool operator == (const modular &rhs) const { return value == rhs.value; }
  constexpr bool operator != (const modular &rhs) const { return value != rhs.value; }
  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) {
    return stream << rhs.value;
  }

};

using m32 = modular<998244353>;

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

template <class T, size_t N, size_t I = 0>
decltype(auto) gen_vec(const size_t (&list)[N], typename std::enable_if<(I == N), const T&>::type value = T()) { 
  return value; 
}

template <class T, size_t N, size_t I = 0>
decltype(auto) gen_vec(const size_t (&list)[N], typename std::enable_if<(I != N), const T&>::type value = T()) { 
  return std::vector(list[I], gen_vec<T, N, I + 1>(list, value)); 
}

#ifdef LOCAL
#include <iostream>
#include <iomanip>
#include <fstream>
#include <sstream>
#include <ctime>

struct debug_support {

  std::ofstream file;
  std::stringstream to_str_helper;
  clock_t start_time;
  size_t str_width;

  debug_support() {
    file.open("debug.txt");
    if (!file.is_open()) {
      std::cerr << "\033[31m failed to open the file 'debug.txt' \033[0m \n";
      std::exit(EXIT_FAILURE);
    }
    file << "\n<debug output file>\n\n";
    to_str_helper << std::boolalpha;
    to_str_helper << std::fixed;
    setwidth(3);
    setprecision(6);
    settime();
  }
  ~debug_support() {
    file.close(); 
  }

  void setwidth(size_t x) {
    str_width = x;
  }
  void setprecision(size_t x) {
    to_str_helper << std::setprecision(x);
  }
  void settime() {
    start_time = std::clock();
  }

  std::string to_str(char c) { 
    return std::string("'") + c + "'"; 
  }
  std::string to_str(const std::string &s) { 
    return std::string("\"") + s + "\""; 
  }
  std::string to_str(const char *s) { 
    return std::string("\"") + s + "\""; 
  }

  template <class T, class U>
  std::string to_str(const std::pair<T, U> &x) { 
    return "(" + to_str(x.first) + ", " + to_str(x.second) + ")"; 
  }
  template <class T, size_t I>
  typename std::enable_if<(I + 1 == std::tuple_size<T>::value), std::string>::type to_str_tuple(const T &x) { 
    return to_str(std::get<I>(x)); 
  } 
  template <class T, size_t I>
  typename std::enable_if<(I + 1 != std::tuple_size<T>::value), std::string>::type to_str_tuple(const T &x) { 
    return to_str(std::get<I>(x)) + ", " + to_str_tuple<T, I + 1>(x);
  } 
  template <class... Args>
  std::string to_str(const std::tuple<Args...> &x) {
    return "(" + to_str_tuple<std::tuple<Args...>, 0>(x) + ")";
  }

  template <class T>
  std::string to_str(const T &x) {
    to_str_helper << x;
    std::string s;
    std::getline(to_str_helper, s);
    to_str_helper.str("");
    to_str_helper.clear(std::stringstream::goodbit);
    return s;
  }
  template <class T, class U, class... Args>
  std::string to_str(const T &x, const U &y, const Args&... args) { 
    return x == y ? "__" : to_str(x, args...); 
  }

  std::string fix_str(const std::string &s) {
    if (s.size() >= str_width) return s;
    return std::string(str_width - s.size(), ' ') + s;
  }

  template<typename T, typename _ = void>
  struct has_iterator: public std::false_type {};
  template<typename T>
  struct has_iterator<T, typename std::conditional<false, typename T::iterator, void>::type>: public std::true_type {};

  template <class T, class... Args>
  typename std::enable_if<has_iterator<typename T::value_type>::value == true, std::string>::type 
  to_str_container(const T &x, const Args&... args) {
    std::string s;
    for (const auto &v: x) {
      s += to_str_container(v, args...);
    }
    return s + '\n';
  }
  template <class T, class... Args>
  typename std::enable_if<has_iterator<typename T::value_type>::value == false, std::string>::type 
  to_str_container(const T &x, const Args&... args) {
    std::string s = "{ ";
    bool f = false;
    for (const auto &v: x) {
      if (f) s += ", ";
      f = true;
      s += fix_str(to_str(v, args...));
    }
    return s + " }\n";
  }

  template <class T>
  void print(const T &x) { 
    file << to_str(x) << std::endl;
  }
  template <class T, class... Args>
  void print(const T &x, const Args&... args) {
    file << to_str(x) << ", ";
    print(args...);
  }

  template <class T, class... Args>
  void print_container(const T &x, const Args&... args) {
    file << to_str_container(x, args...) << std::endl;
    setwidth(3);
  }

} debugger;

#define show(...)\
  do {\
    debugger.file << "<line:" << std::setw(4) << __LINE__ << ">";\
    debugger.file << " [" << #__VA_ARGS__ << "]: ";\
    debugger.print(__VA_ARGS__);\
  } while (false)

#define show_c(x, ...)\
 do {\
    debugger.file << "\n<line:" << std::setw(4) << __LINE__ << ">";\
    debugger.file << " [" << #x << "]";\
    if (std::string(#__VA_ARGS__).empty()) debugger.file << ":\n";\
    else debugger.file << " (ignore " << #__VA_ARGS__ << "):\n";\
    debugger.print_container(x __VA_OPT__(,) __VA_ARGS__);\
 } while (false)

#define show_e()\
  do {\
    double d = static_cast<double>(std::clock() - debugger.start_time);\
    debugger.file << "<line:" << std::setw(4) << __LINE__ << ">";\
    debugger.file << " elapsed time: " << d * 1000 / CLOCKS_PER_SEC << "ms" << std::endl;\
  } while (false)

#else
#define show(...) ((void) 0)
#define show_c(...) ((void) 0)
#define show_e() ((void) 0)
#endif

int main() {
  std::string S;
  std::cin >> S;
  std::reverse(S.begin(), S.end());
  S.push_back('0');
  std::vector<i32> vec;
  i32 all = 0;
  {
    i32 cur = 0;
    for (auto c: S) {
      if (c == '0') {
        vec.push_back(cur);
        cur = 0;
      }
      else {
        ++cur;
        ++all;
      }
    }
  }
  i32 K;
  std::cin >> K;
  chmin(K, all);
  i32 N = vec.size();

  //*  <naive solution>
  auto dp = gen_vec<m32>({ N + 1, 2 * K + 1, all + 1 });
  dp[0][0][0] = m32(1);
  i32 cur = 0;
  for (auto i: range(0, N)) {
    i32 ncur = cur + vec[i];
    for (auto j: range(0, 2 * K + 1)) {
      for (auto l: range(0, cur + 1)) {
        for (auto k: range(0, ncur + 1)) {
          if (l + k > ncur) {
            continue;
          }
          if (j + std::abs(k - vec[i]) > 2 * K) {
            continue;
          }
          dp[i + 1][j + std::abs(k - vec[i])][l + k] += dp[i][j][l];
        }
      }
    }
    cur = ncur;
  }
  m32 ans;
  for (auto j: range(0, 2 * K + 1)) {
    ans += dp[N][j][all];
  }
  std::cout << ans << '\n';
  // */

  return 0;
}


Measured memory_bytes: 31548