#include <bits/stdc++.h>
using namespace std;

#define INF_LL (int64)1e18
#define INF (int32)1e9
#define REP(i, n) for(int64 i = 0;i < (n);i++)
#define FOR(i, a, b) for(int64 i = (a);i < (b);i++)
#define all(x) x.begin(),x.end()
#define fs first
#define sc second

using int32 = int_fast32_t;
using uint32 = uint_fast32_t;
using int64 = int_fast64_t;
using uint64 = uint_fast64_t;
using PII = pair<int32, int32>;
using PLL = pair<int64, int64>;

const double eps = 1e-10;

template<typename A, typename B>inline void chmin(A &a, B b){if(a > b) a = b;}
template<typename A, typename B>inline void chmax(A &a, B b){if(a < b) a = b;}

template<typename T>
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 U,typename... V>
typename enable_if<is_same<T, U>::value!=0>::type
fill_v(U &u,const V... v){u=U(v...);}

template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value==0>::type
fill_v(U &u,const V... v){
	for(auto &e:u) fill_v<T>(e,v...);
}

template<::std::uint_fast64_t mod>
class ModInt{
private:
  using value_type = ::std::uint_fast64_t;
  value_type n;
public:
  ModInt() : n(0) {}
  ModInt(value_type n_) : n(n_ % mod) {}
  ModInt(const ModInt& m) : n(m.n) {}

  template<typename T>
  explicit operator T() const { return static_cast<T>(n); }
  value_type get() const { return n; }

  friend ::std::ostream& operator<<(::std::ostream &os, const ModInt<mod> &a) {
    return os << a.n;
  }

  friend ::std::istream& operator>>(::std::istream &is, ModInt<mod> &a) {
    value_type x;
    is >> x;
    a = ModInt<mod>(x);
    return is;
  }

  bool operator==(const ModInt& m) const { return n == m.n; }
  bool operator!=(const ModInt& m) const { return n != m.n; }
  ModInt& operator*=(const ModInt& m){ n = n * m.n % mod; return *this; }

  ModInt pow(value_type b) const{
    ModInt ans = 1, m = ModInt(*this);
    while(b){
      if(b & 1) ans *= m;
      m *= m;
      b >>= 1;
    }
    return ans;
  }

  ModInt inv() const { return (*this).pow(mod-2); }
  ModInt& operator+=(const ModInt& m){ n += m.n; n = (n < mod ? n : n - mod); return *this; }
  ModInt& operator-=(const ModInt& m){ n += mod - m.n; n = (n < mod ? n : n - mod); return *this; }
  ModInt& operator/=(const ModInt& m){ *this *= m.inv(); return *this; }
  ModInt operator+(const ModInt& m) const { return ModInt(*this) += m; }
  ModInt operator-(const ModInt& m) const { return ModInt(*this) -= m; }
  ModInt operator*(const ModInt& m) const { return ModInt(*this) *= m; }
  ModInt operator/(const ModInt& m) const { return ModInt(*this) /= m; }
  ModInt& operator++(){ n += 1; return *this; }
  ModInt& operator--(){ n -= 1; return *this; }
  ModInt operator++(int){
    ModInt old(n);
    n += 1;
    return old;
  }
  ModInt operator--(int){
    ModInt old(n);
    n -= 1;
    return old;
  }
  ModInt operator-() const { return ModInt(mod-n); }
};

template<::std::size_t size, ::std::uint_fast64_t mod=1000000007>
class Factorial{
private:
  using value_type = ModInt<mod>;
  ::std::vector<value_type> fact, inv;
public:
  Factorial() : fact(size+1, 1), inv(size+1, 1){
    for(::std::size_t i = 1; i <= size; ++i){
      fact[i] = fact[i-1] * value_type(i);
      inv[i] = fact[i].inv();
    }
  }

  value_type comb(::std::int64_t a, ::std::int64_t b){
    assert(a >= b);
    assert(b >= 0);
    return fact[a]*inv[b]*inv[a-b];
  }

  value_type& operator[](::std::size_t k){ return fact[k]; }
};

constexpr int64 mod = 998244353;
using Mint = ModInt<mod>;
Factorial<11234, mod> f;

int main(void){
	cin.tie(0);
	ios::sync_with_stdio(false);

	string S;
	int64 K;
	cin >> S >> K;
	vector<int64> c({0});
	int64 one = 0;
	REP(i, S.size()) {
	  if (S[i] == '0') {
	    c.push_back(0);
	  } else {
	    one++;
	    c.back()++;
	  }
	}
	K = min(K, (int64)300);
  c.push_back(0);
	auto dp = make_v<Mint>(c.size()+1, one+2, K+2, 2);
	dp[0][c[0]][0][1] = 1;
	int64 sum = 0;
	REP(i, c.size()-1) {
	  FOR(j, sum, one + 1) {
	    REP(k, K+1) {
	      if (j > 0) {
          dp[i][j][k][0] += dp[i][j - 1][k][0];
        }

	      if (j + 1 <= one && k + 1 <= K) {
	        dp[i][j + 1][k + 1][1] += dp[i][j][k][1];
        }

	      if (j >= sum + c[i]) {
	        if (j + c[i + 1] <= one)
  	        dp[i+1][j + c[i + 1]][k][1] += dp[i][j][k][0] + dp[i][j][k][1];
	        if (max(j, sum + c[i] + c[i+1]) <= one) {
            dp[i + 1][max(j, sum + c[i] + c[i + 1])][k][0] += dp[i][j][k][0] + dp[i][j][k][1];
            if (min(j + c[i + 1], sum + c[i] + c[i + 1] + k) <= one)
              dp[i + 1][min(j + c[i + 1], sum + c[i] + c[i + 1] + k)][k][0] -= dp[i][j][k][0] + dp[i][j][k][1];
          }
//          cout << i << " " << j << " " << k << ": " << max(j, sum + c[i] + c[i+1]) << " " << min(j + c[i=1], sum + c[i] + c[i+1] + k) << endl;
        }
//	      cout << i << " " << j << " " << k << " " << 0 << ": " << dp[i][j][k][0] << endl;
//        cout << i << " " << j << " " << k << " " << 1 << ": " << dp[i][j][k][1] << endl;
	    }
	  }
    sum += c[i];
	}
	Mint res = 0;
  REP(k, K + 1) {
    res += dp[c.size() - 2][one][k][0] + dp[c.size() - 2][one][k][1];
  }
	cout << res << endl;
}


Measured memory_bytes: 388324