/*Bismillahir Rahmanir Rahim*///{
#include <bits/stdc++.h>
#include <ext/numeric>
using namespace std; using __gnu_cxx::power;
using ll = long long; using ull = unsigned long long; using ld = long double;
const ll llinf = (1ll<<61)-1; const double eps = 1e-6, ldeps = 1e-9;
struct Dbg { static constexpr auto &os = cout;   // replace by cerr in interactive.
template<class C> static auto o(C *x)->decltype(os << *x, 0);
template<class C> static char o(...);
template<class C> typename enable_if<sizeof o<C>(0)!=1,Dbg&>::type operator<<(const C &x) {os<<x; return *this;}
template<class C> Dbg &dump(C b, C e) {
    for (struct{C i;int j;} i={(*this<<"\n[",b),0}; i.i!=e and i.j<26; i.i++, i.j++) *this<<", "+2*(i.i==b)<<*i.i;
    return *this << ']';
}
template<class C> typename enable_if<sizeof o<C>(0)==1, Dbg&>::type operator<<(const C &x) {
    return dump(begin(x), end(x));
}
template<class C, size_t X> typename enable_if<!is_same<C, const char>::value, Dbg&>::type operator<<(C (&x)[X]) {
    return dump(begin(x), end(x));
}
template<class B, class C> Dbg &operator<<(const pair<B, C> &x) {return *this<<'{'<<x.first<<", "<<x.second<<'}';}
Dbg &operator<<(ostream&(*x)(std::ostream&)) { os << x; return *this; }
} dbg;
void err(istringstream *iss) { delete iss; }
template<class C, class... Args> void err(istringstream *iss, const C &val, const Args &... args) {
    string name; *iss >> name; if (name.back()==',') name.pop_back();
    dbg << name << " = " << val << "; ", err(iss, args...);
}
#define bug(args...) dbg << __LINE__ << ": ", err(new istringstream(#args), args), dbg << endl
#define cbug(a, args...) if (a) bug(args);
#define ASSERT(a, o, b, args...) if (!((a)o(b))) bug(a, b, ##args), assert((a)o(b));
#define sl(a) int(strlen(a))
#define sz(a) int(a.size())
int T, Q, cn;//}
const int inf = 998244353, mxn = 305;

template<class C, class D> C& operator +=(C &x, const D &y) { return x = x+y; }//{
template<class C, class D> C& operator -=(C &x, const D &y) { return x = x-y; }
template<class C, class D> C& operator *=(C &x, const D &y) { return x = x*y; }
template<class C, class D> bool operator ==(const C &ls, const D &rs) { return !(ls<rs or rs<ls); }
template<class C, class D> bool operator !=(const C &ls, const D &rs) { return !(rs==ls); }
template<class C, class D> bool operator >(const C &ls, const D &rs) { return (rs<ls); }
template<class C, class D> bool operator <=(const C &ls, const D &rs) { return !(rs<ls); }
template<class C, class D> bool operator >=(const C &ls, const D &rs) { return !(ls<rs); }

struct Int// Make sure to not do any operation with non-modded(except *, which must be int, *1 to mod forcefully)
{
    int x;
    Int() = default;
    Int(const int &rs) : x(rs + (rs>=0 ? 0 : inf)) {};
    Int operator -() { return inf-*this; }
    // Int operator ~() = delete;
    Int operator ~() { return power(*this, inf-2); }
    Int operator +(const Int &rs) const { return x+rs.x>=inf ? x+rs.x-inf : x+rs.x; }
    Int operator -(const Int &rs) const { return x-rs.x<0 ? x-rs.x+inf : x-rs.x; }
    Int operator *(const Int &rs) const { return int(x*ll(rs.x)%inf); }
    Int operator <<(const int &rs) { return rs==1 ? *this+*this : *this*Int{1<<rs}; }
    Int& operator <<=(const int &rs) { return *this = *this<<rs; }
    Int& operator >>=(const int &rs) { return x>>=rs, *this; }  // only for power()
    Int& operator ++() { return *this += 1; }
    Int& operator --() { return *this -= 1; }
    Int operator ++(int) { Int ret = x; ++*this; return ret; }
    Int operator --(int) { Int ret = x; --*this; return ret; }
    friend istream& operator >>(istream &is, Int &rs) { return is>>rs.x; }
    friend ostream& operator <<(ostream &os, const Int &rs) { return os<<rs.x; }
    friend Int operator +(const Int &ls, const int &rs) { return ls+Int(rs); }
    friend Int operator +(const int &ls, const Int &rs) { return Int(ls)+rs; }
    friend Int operator -(const Int &ls, const int &rs) { return ls-Int(rs); }
    friend Int operator -(const int &ls, const Int &rs) { return Int(ls)-rs; }
    friend Int operator *(const Int &ls, const int &rs) { return ls*Int(rs); }
    friend Int operator *(const int &ls, const Int &rs) { return Int(ls)*rs; }
    bool operator <(const Int &rs) const { return x<rs.x; }
    friend bool operator <(const int &ls, const Int &rs) { return ls<rs.x; }
    friend bool operator <(const Int &ls, const int &rs) { return ls.x<rs; }
};

Int operator""_i(unsigned long long x) { return {int(x)}; }//}

int n, K, cz, cs[mxn];
char s[mxn];
vector<int> zeros;

Int dp[mxn][mxn][mxn], csdpmove[mxn][mxn][mxn], csdpmoveMinusTan[mxn][mxn][mxn];

signed main() { cin.tie(0)->sync_with_stdio(0); cin.exceptions(cin.failbit); cout.precision(11), cout.setf(ios::fixed);
/*
1101010010101101110111100011011111011000111101110101010010101010101 20
*/
    cin >> s >> K;
    n = sl(s), K = min(K, n);
    for (int i = 0; i < n; i++) {
        if (s[i] == '0') zeros.push_back(i);
    }
    cz = sz(zeros);
    for (int i = n-1; i >= 0; i--) {
        cs[i] += cs[i+1], cs[i] += s[i] == '1';
    }

    for (int at = cz; at>=0; at--) {
        for (int tan = 0; tan<=K; tan++) {
            for (int move = tan; move<=K; move++) {
                int eo = cs[at ? zeros[at-1] : 0];
                if (eo < tan) continue;
                auto &ret = dp[at][tan][move];
                if (at==cz) {
                    ret = 1;
                    continue;
                }
                int epo = eo-cs[zeros[at]], cpo = max(0, epo-tan), ntan = tan-min(tan, epo);
                int mxpo = eo-tan;
                ret += csdpmove[at+1][move][ntan+min(epo, mxpo)-cpo]-(ntan ? csdpmove[at+1][move][ntan-1] : 0);
                // for (int l = cpo; l <= min(epo, mxpo); l++) {
                //     ret += dp[at+1][ntan+l-cpo][move];
                // }
                if (epo >= mxpo) continue;
                ret += csdpmoveMinusTan[at+1][move-epo-(ntan-cpo)][min(move+mxpo-epo, K)]-csdpmoveMinusTan[at+1][move-epo-(ntan-cpo)][move];
                // for (int l = epo+1; l <= mxpo; l++) {
                //     if (move+l-epo > K) break;
                //     ret += dp[at+1][ntan+l-cpo][move+l-epo];
                // }
            }
        }
        for (int tan = 0; tan<=K; tan++) {
            for (int move = tan; move<=K; move++) {
                csdpmove[at][move][tan] = (tan ? csdpmove[at][move][tan-1] : 0)+dp[at][tan][move];
                csdpmoveMinusTan[at][move-tan][move] = (move ? csdpmoveMinusTan[at][move-tan][move-1] : 0)+dp[at][tan][move];
            }
        }
    }
    cout << dp[0][0][0] << '\n';
}

Measured memory_bytes: 126292