#include <bits/stdc++.h>

#if MYDEBUG
#include "lib/cp_debug.hpp"
#else
#define DBG(...) ;
#endif
#if __cplusplus <= 201402L
template <typename T>
T gcd(T a, T b) { return ((a % b == 0) ? b : gcd(b, a % b)); }
template <typename T>
T lcm(T a, T b) { return a / gcd(a, b) * b; }
#endif
using LL = long long;
constexpr LL LINF = 334ll << 53;
constexpr int INF = 15 << 26;
constexpr LL MOD = 998244353;

namespace Problem {
using namespace std;
template <long long Mod = MOD>
class Modint {
 public:
  long long v;

  Modint(const Modint &x) { v = x.v; }
  explicit Modint(int x) {
    if (x < 0 or Mod <= x) x %= Mod;
    if (x < 0) x += Mod;
    v = x;
  }
  explicit Modint(long long x) {
    if (x < 0 or Mod <= x) x %= Mod;
    if (x < 0) x += Mod;
    v = x;
  }
  explicit Modint(unsigned x) {
    if (Mod <= x) x %= Mod;
    v = x;
  }
  explicit Modint(unsigned long long x) {
    if (Mod <= x) x %= Mod;
    v = x;
  }
  template <typename T>
  explicit Modint(T x) {
    if (x < 0 or Mod <= x) x %= Mod;
    v = x;
  }
  Modint() : v(0) {}
  long long get() const { return v; }
  Modint mpow(Modint &n) const { return mpow(n.v); }
  Modint mpow(long long n) const {
    long long i = 1, p = v;
    Modint ret(1);
    while (i <= n) {
      if (i & n) ret *= p;
      i = (i << 1);
      p = (p * p) % Mod;
    }
    return ret;
  }
  Modint operator-() const { return (v ? Modint(Mod - v) : Modint(0)); }
  explicit operator int() const { return v; }
  explicit operator long long() const { return v; }
  Modint &operator+=(const Modint &a) {
    v = (v + a.v);
    if (v >= Mod) v -= Mod;
    return *this;
  }
  Modint &operator-=(const Modint &a) {
    v = (v - a.v);
    if (v < 0) v += Mod;
    return *this;
  }
  Modint &operator*=(const Modint &a) {
    v = (v * a.v) % Mod;
    return *this;
  }
  Modint &operator/=(const Modint &a) {
    v = (v * a.mpow(Mod - 2).v) % Mod;
    return *this;
  }
  template <class T>
  Modint &operator+=(const T &a) {
    v = (v + Modint(a).v);
    if (v >= Mod) v -= Mod;
    return *this;
  }
  template <class T>
  Modint &operator-=(const T &a) {
    v = (v - Modint(a).v);
    if (v < 0) v += Mod;
    return *this;
  }
  template <class T>
  Modint &operator*=(const T &a) {
    v = (v * Modint(a).v) % Mod;
    return *this;
  }
  template <class T>
  Modint &operator/=(const T &a) {
    v = (v * Modint(a).mpow(Mod - 2).v) % Mod;
    return *this;
  }
  friend Modint operator+(const Modint &a, const Modint &b) {
    return Modint(a) += b;
  }
  friend Modint operator-(const Modint &a, const Modint &b) {
    return Modint(a) -= b;
  }
  friend Modint operator*(const Modint &a, const Modint &b) {
    return Modint(a) *= b;
  }
  friend Modint operator/(const Modint &a, const Modint &b) {
    return Modint(a) /= b;
  }
  template <class T, class U>
  friend Modint operator+(const T &a, const U &b) {
    return Modint(a) += Modint(b);
  }
  template <class T, class U>
  friend Modint operator-(const T &a, const U &b) {
    return Modint(a) -= Modint(b);
  }
  template <class T, class U>
  friend Modint operator*(const T &a, const U &b) {
    return Modint(a) *= Modint(b);
  }
  template <class T, class U>
  friend Modint operator/(const T &a, const U &b) {
    return Modint(a) /= Modint(b);
  }
};

template <long long M>
ostream &operator<<(ostream &os, const Modint<M> m) {
  return os << m.v;
}

class Solver {
 public:
  string s;
  int ub, l;
  Solver(string s, LL k) : s(s), ub(k), l(s.length()){};

  void solve() {
    vector<int> seq(1);
    int c0 = 0, c1 = 0;
    for (int i = 0; i < l; ++i) {
      if (s[i] == '0') {
        c0++;
        seq.push_back(0);
      } else {
        c1++;
        seq.back()++;
      }
    }
    vector<vector<Modint<>>> dp(400, vector<Modint<>>(400));
    ub = min(350, ub);
    dp[0][0] = Modint<>(1);
    int sum = 0;
    for (int i = 0; i < (int)seq.size(); ++i) {
      sum += seq[i];
      vector<vector<Modint<>>> dp2(400, vector<Modint<>>(400));
      vector<vector<Modint<>>> dp3(400, vector<Modint<>>(400));
      vector<vector<Modint<>>> dp4(400, vector<Modint<>>(400));
      for (int j = 0; j <= c1; ++j) {
        for (int k = 0; k <= ub; ++k) {
          int U = min(l - j, seq[i] + ub - k);
          int L = max(0, sum - j);
          if (L < seq[i]) {
            if (seq[i] < U) {
              dp2[j + L][k] += dp[j][k];
              dp2[j + seq[i]][k] -= dp[j][k];
              dp3[j + seq[i]][k] += dp[j][k];
              dp3[j + U + 1][k + U + 1 - seq[i]] -= dp[j][k];
            } else {
              dp2[j + L][k] += dp[j][k];
              dp2[j + U + 1][k] -= dp[j][k];
            }
          } else {
            dp3[j + L][k + L - seq[i]] += dp[j][k];
            dp3[j + U + 1][k + U + 1 - seq[i]] -= dp[j][k];
          }
        }
      }
      for (int j = 0; j <= c1; ++j) {
        for (int k = 0; k <= ub; ++k) {
          if (j > 0) dp2[j][k] += dp2[j - 1][k];
          if (j > 0 && k > 0) dp3[j][k] += dp3[j - 1][k - 1];
        }
      }
      for (int j = 0; j <= c1; ++j) {
        for (int k = 0; k <= ub; ++k) {
          dp4[j][k] = dp2[j][k] + dp3[j][k];
        }
      }
      swap(dp, dp4);
    }
    Modint<> ans(0);
    for (int k = 0; k <= ub; ++k) {
      ans += dp[c1][k];
    }
    cout << ans << endl;
  }
};  // namespace Problem

}  // namespace Problem

int main() {
  std::cin.tie(0);
  std::ios_base::sync_with_stdio(false);
  // std::cout << std::fixed << std::setprecision(12);
  std::string s;
  long long n = 0;
  std::cin >> s >> n;

  Problem::Solver sol(s, n);
  sol.solve();
  return 0;
}


Measured memory_bytes: 8344