//#define NDEBUG

#pragma region cp_template

#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <iostream>
#include <utility>
#include <vector>

namespace n91 {

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

struct rep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { ++i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
struct revrep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { --i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
template <class T> auto md_vec(const usize n, const T &value) {
  return std::vector<T>(n, value);
}
template <class... Args> auto md_vec(const usize n, Args... args) {
  return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> constexpr T difference(const T &a, const T &b) noexcept {
  return a < b ? b - a : a - b;
}
template <class T> void chmin(T &a, const T &b) noexcept {
  if (b < a)
    a = b;
}
template <class T> void chmax(T &a, const T &b) noexcept {
  if (a < b)
    a = b;
}
template <class F> class rec_lambda {
  F f;

public:
  rec_lambda(F &&f) : f(std::move(f)) {}
  template <class... Args> auto operator()(Args &&... args) const {
    return f(*this, std::forward<Args>(args)...);
  }
};
template <class F> auto make_rec(F &&f) { return rec_lambda<F>(std::move(f)); }
template <class T> T scan() {
  T ret;
  std::cin >> ret;
  return ret;
}
constexpr char eoln = '\n';
template <class T> T ceildiv(const T &l, const T &r) {
  return l / r + (l % r != 0 ? 1 : 0);
}

} // namespace n91

#pragma endregion cp_template

#include <cstdint>

template <std::uint_fast64_t mod> class modint {
  using u64 = std::uint_fast64_t;

public:
  u64 v;

  constexpr modint(const u64 x = 0) noexcept : v(x % mod) {}
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    v += rhs.v;
    if (v >= mod)
      v -= mod;
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (v < rhs.v)
      v += mod;
    v -= rhs.v;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    v = v * rhs.v % mod;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = mod - 2;
    while (exp != 0) {
      if (exp % 2 != 0)
        *this *= rhs;
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};

namespace n91 {

void main_() {
  /*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  using mint = modint<998244353>;

  const std::string s = scan<std::string>();
  const usize n = s.size();
  const usize k = std::min(scan<usize>(), n);

  std::vector<usize> ones;
  {
    usize c = 0;
    for (const auto e : s) {
      if (e == '1') {
        c += 1;
      } else {
        ones.push_back(c);
        c = 0;
      }
    }
    ones.push_back(c);
  }

  const usize m = ones.size();

  auto dp = md_vec(k + 2, k + 2, mint(0));
  dp[0][0] = 1;
  for (const usize loop : revrep(0, m)) {
    const auto one = ones[loop];

    auto nx = md_vec(k + 2, k + 2, mint(0));
    for (const usize j : rep(0, k + 1)) {
      for (const usize l : rep(0, j + 1)) {
        const auto e = dp[j][l];
        // yoko
        {
          nx[j][l] += e;
          nx[j][k + 1] -= e;
          nx[j + 1][l] -= e;
          nx[j + 1][k + 1] += e;
        }
        // tate
        {
          nx[j + 1][l] += e;
          nx[j + 1][l + 1] -= e;
          nx[std::min(k + 1, j + one + 1)][l] -= e;
          nx[std::min(k + 1, j + one + 1)][l + 1] += e;
        }
      }
    }

    for (const usize j : rep(0, k + 2)) {
      for (const usize l : rep(0, k + 1)) {
        nx[j][l + 1] += nx[j][l];
      }
    }

    for (const usize j : rep(0, k + 1)) {
      for (const usize l : rep(0, k + 2)) {
        nx[j + 1][l] += nx[j][l];
      }
    }

    dp = std::move(nx);
  }

  mint ans = 0;
  for (const usize j : rep(0, k + 1)) {
    ans += dp[j][j];
  }

  std::cout << ans.v << eoln;
}

} // namespace n91

int main() {
  n91::main_();
  return 0;
}


Measured memory_bytes: 4672